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| Some of the finite structures considered in [[graph theory]] have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the [[Petersen graph]], a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts.
| | Nice to satisfy you, my name is Araceli Oquendo but I don't like when people use my complete title. Bookkeeping is what she does. Alabama is exactly where he and his wife reside and he has every thing that he requirements there. To keep birds is one of the issues he enjoys most.<br><br>My web-site [http://gshappy.marubaram.wo.tc/xe/?document_srl=256061 http://gshappy.marubaram.wo.tc/] |
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| ==Individual graphs==
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| <center>
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| <gallery perrow="5">
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| File:Balaban 10-cage alternative drawing.svg|[[Balaban 10-cage]]
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| File:Balaban 11-cage.svg|[[Balaban 11-cage]]
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| File:Bidiakis cube.svg|[[Bidiakis cube]]
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| File:Brinkmann graph LS.svg|[[Brinkmann graph]]
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| File:Bull graph.circo.svg|[[Bull graph]]
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| File:Butterfly graph.svg|[[Butterfly graph]]
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| File:Chvatal graph.draw.svg|[[Chvátal graph]]
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| File:Diamond graph.svg|[[Diamond graph]]
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| File:Dürer graph.svg|[[Dürer graph]]
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| File:Ellingham-Horton 54-graph.svg|[[Ellingham–Horton 54-graph]]
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| File:Ellingham-Horton 78-graph.svg|[[Ellingham–Horton 78-graph]]
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| File:Errera graph.svg|[[Errera graph]]
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| File:Franklin graph.svg|[[Franklin graph]]
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| File:Frucht planar Lombardi.svg|[[Frucht graph]]
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| File:Goldner-Harary graph.svg|[[Goldner–Harary graph]]
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| File:Groetzsch-graph.svg|[[Grötzsch graph]]
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| File:Harries graph alternative_drawing.svg|[[Harries graph]]
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| File:Harries-wong graph.svg|[[Harries–Wong graph]]
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| File:Herschel graph no col.svg|[[Herschel graph]]
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| File:Hoffman graph.svg|[[Hoffman graph]]
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| File:Holt graph.svg|[[Holt graph]]
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| File:Horton graph.svg|[[Horton graph]]
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| File:Kittell graph.svg|[[Kittell graph]]
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| File:Markström-Graph.svg|[[Erdős–Gyárfás conjecture|Markström graph]]
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| File:McGee graph.svg|[[McGee graph]]
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| File:Meredith graph.svg|[[Meredith graph]]
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| File:Moser spindle.svg |[[Moser spindle]]
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| File:Sousselier graph.svg|[[Sousselier graph]]
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| File:Poussin graph.svg|[[Poussin graph]]
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| File:Robertson graph.svg|[[Robertson graph]]
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| File:Tutte fragment.svg|[[Tutte's fragment]]
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| File:Tutte graph.svg|[[Tutte graph]]
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| File:Young-Fibonacci.svg|[[Young–Fibonacci lattice|Young–Fibonacci graph]]
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| File:Wagner graph ham.svg|[[Wagner graph]]
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| File:Wiener-Araya.svg|[[Wiener–Araya graph]]
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| </gallery>
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| </center>
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| | |
| ==Highly symmetric graphs==
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| ===Strongly regular graphs===
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| The [[strongly regular graph]] on ''v'' vertices and rank ''k'' is usually denoted srg(''v,k'',λ,μ).
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| <center>
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| <gallery>
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| File:Clebsch graph.svg|[[Clebsch graph]]
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| File:Petersen1 tiny.svg|[[Petersen graph]]
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| File:Hall janko graph.svg|[[Hall–Janko graph]]
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| File:Hoffman singleton graph circle2.gif|[[Hoffman–Singleton graph]]
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| File:Higman Sims Graph.svg|[[Higman–Sims graph]]
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| File:Paley13 no label.svg|[[Paley graph]] of order 13
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| File:Shrikhande graph symmetrical.svg|[[Shrikhande graph]]
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| File:Schläfli graph.svg|[[Schläfli graph]]
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| File:Brouwer Haemers graph.svg|[[Brouwer–Haemers graph]]
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| File:Local mclaughlin graph.svg|[[Local McLaughlin graph]]
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| File:Perkel graph embeddings.svg|[[Perkel graph]]
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| File:Gewirtz graph embeddings.svg|[[Gewirtz graph]]
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| </gallery>
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| </center>
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| | |
| ===Symmetric graphs===
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| A [[symmetric graph]] is one in which there is a symmetry ([[graph automorphism]]) taking any ordered pair of adjacent vertices to any other ordered pair; the [[Foster census]] lists all small symmetric 3-regular graphs. Every strongly regular graph is symmetric, but not vice versa.
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| <center>
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| <gallery>
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| File:Heawood Graph.svg|[[Heawood graph]]
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| File:Möbius–Kantor unit distance.svg|[[Möbius–Kantor graph]]
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| File:Pappus graph.svg|[[Pappus graph]]
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| File:DesarguesGraph.svg|[[Desargues graph]]
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| File:Nauru graph.svg|[[Nauru graph]]
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| File:Coxeter graph.svg|[[Coxeter graph]]
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| File:Tutte eight cage.svg|[[Tutte–Coxeter graph]]
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| File:Dyck graph.svg|[[Dyck graph]]
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| File:Klein graph.svg|[[Klein graphs|Klein graph]]
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| File:Foster graph.svg|[[Foster graph]]
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| File:Biggs-Smith graph.svg|[[Biggs–Smith graph]]
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| File:Rado graph.svg|The [[Rado graph]]
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| </gallery>
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| </center>
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| ===Semi-symmetric graphs===
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| <center>
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| <gallery>
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| File:Folkman_Lombardi.svg|[[Folkman graph]]
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| File:Gray graph hamiltonian.svg|[[Gray graph]]
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| File:Ljubljana graph hamiltonian.svg|[[Ljubljana graph]]
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| File:Tutte 12-cage.svg|[[Tutte 12-cage]]
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| </gallery>
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| </center>
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| ==Graph families==
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| ===Complete graphs===
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| The [[complete graph]] on <math>n</math> vertices is often called the ''<math>n</math>-clique'' and usually denoted <math>K_n</math>, from German ''komplett''.<ref>David Gries and Fred B. Schneider, ''A Logical Approach to Discrete Math'', Springer, 1993, p 436.</ref>
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| <center>
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| <gallery>
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| File:Complete graph K1.svg|<math>K_1</math>
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| File:Complete graph K2.svg|<math>K_2</math>
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| File:Complete graph K3.svg|<math>K_3</math>
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| File:Complete graph K4.svg|<math>K_4</math>
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| File:Complete graph K5.svg|<math>K_5</math>
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| File:Complete graph K6.svg|<math>K_6</math>
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| File:Complete graph K7.svg|<math>K_7</math>
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| File:Complete graph K8.svg|<math>K_8</math>
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| </gallery>
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| </center>
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| ===Complete bipartite graphs===
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| The [[complete bipartite graph]] is usually denoted <math>K_{n,m}</math>. For <math>n=1</math> see the section on star graphs. The graph <math>K_{2,2}</math> equals the 4-cycle <math>C_4</math> (the square) introduced below.
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| <center>
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| <gallery>
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| File:Biclique K 2 3.svg|<math>K_{2,3}</math>
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| File:Biclique K 3 3.svg|<math>K_{3,3}</math>, the [[water, gas, and electricity|utility graph]]
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| File:Biclique K 2 4.svg|<math>K_{2,4}</math>
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| File:Biclique K 3 4.svg|<math>K_{3,4}</math>
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| </gallery>
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| </center>
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| ===Cycles===
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| The [[cycle graph]] on <math>n</math> vertices is called the ''n-cycle'' and usually denoted <math>C_n</math>. It is also called a ''cyclic graph'', a ''polygon'' or the ''n-gon''. Special cases are the ''triangle'' <math>C_3</math>, the ''square'' <math>C_4</math>, and then several with Greek naming ''pentagon'' <math>C_5</math>, ''hexagon'' <math>C_6</math>, etc.
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| <center>
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| <gallery>
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| File:Complete graph K3.svg|<math>C_3</math>
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| File:Circle graph C4.svg|<math>C_4</math>
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| File:Circle graph C5.svg|<math>C_5</math>
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| File:Undirected 6 cycle.svg|<math>C_6</math>
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| </gallery>
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| </center>
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| ===Friendship graphs===
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| The [[friendship graph]] ''F<sub>n</sub>'' can be constructed by joining ''n'' copies of the [[cycle graph]] ''C''<sub>3</sub> with a common vertex.<ref>Gallian, J. A. "Dynamic Survey DS6: Graph Labeling." [[Electronic Journal of Combinatorics]], DS6, 1-58, January 3, 2007. [http://www.combinatorics.org/Surveys/ds6.pdf].</ref>
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| [[File:Friendship graphs.svg|thumb|450px|center|The friendship graphs ''F''<sub>2</sub>, ''F''<sub>3</sub> and ''F''<sub>4</sub>.]]
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| ===Fullerene graphs===
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| In graph theory, the term '''[[fullerene]]''' refers to any 3-[[Regular graph|regular]], [[planar graph]] with all faces of size 5 or 6 (including the external face). It follows from [[Euler characteristic|Euler's polyhedron formula]], ''V'' – ''E'' + ''F'' = 2 (where ''V'', ''E'', ''F'' indicate the number of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and ''V''/2–10 hexagons. Fullerene graphs are the [[Schlegel diagram|Schlegel representations]] of the corresponding fullerene compounds.
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| <center>
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| <gallery>
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| File:Graph of 20-fullerene w-nodes.svg|20-fullerene ([[dodecahedron|dodecahedral]] graph)
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| File:Graph of 24-fullerene w-nodes.svg|24-fullerene ([[Hexagonal truncated trapezohedron]] graph)
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| File:Graph of 26-fullerene 5-base w-nodes.svg|26-fullerene
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| File:Graph of 60-fullerene w-nodes.svg|60-fullerene ([[truncated icosahedron|truncated icosahedral]] graph)
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| File:Graph of 70-fullerene w-nodes.svg|70-fullerene
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| </gallery>
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| </center>
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| An algorithm to generate all the non-isomorphic fullerens with a given number of hexagonal faces has been developed by G. Brinkmann and A. Dress.<ref>{{cite journal |journal=Journal of Algorithms |volume=23 |year=1997 |issue=2 |pages=345–358 |mr=1441972|doi=10.1006/jagm.1996.0806}}</ref> G. Brinkmann also provided a freely available implementation, called [http://cs.anu.edu.au/~bdm/plantri/ fullgen].
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| ===Platonic solids===
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| The [[complete graph]] on four vertices forms the skeleton of the [[tetrahedron]], and more generally the complete graphs form skeletons of [[simplex|simplices]]. The [[hypercube graph]]s are also skeletons of higher dimensional regular [[polytope]]s.
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| <center>
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| <gallery>
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| File:3-cube column graph.svg|[[Hypercube graph|Cube]]<br><math>n=8</math>, <math>m=12</math>
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| File:Octahedral graph.circo.svg|[[Octahedron]]<br><math>n=6</math>, <math>m=12</math>
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| File:Dodecahedral graph.neato.svg|[[Dodecahedron]]<br><math>n=20</math>, <math>m=30</math>
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| File:Icosahedron graph.svg|[[Icosahedron]]<br><math>n=12</math>, <math>m=30</math>
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| </gallery>
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| </center>
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| ===Truncated solids===
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| <center>
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| <gallery>
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| File:3-simplex_t01.svg|[[Truncated tetrahedron]]
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| File:Truncated cubical graph.neato.svg|[[Truncated cube]]
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| File:Truncated octahedral graph.neato.svg|[[Truncated octahedron]]
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| File:Truncated Dodecahedral Graph.svg|[[Truncated dodecahedron]]
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| File:Icosahedron t01 H3.png|[[Truncated icosahedron]]
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| </gallery>
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| </center>
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| ===Snarks===
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| A [[snark (graph theory)|snark]] is a [[bridgeless graph|bridgeless]] [[cubic graph]] that requires four colors in any [[edge coloring]]. The smallest snark is the [[Petersen graph]], already listed above.
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| <center>
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| <gallery perrow="5">
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| File:First Blanusa snark.svg|[[Blanuša snarks|Blanuša snark (first)]]
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| File:Second Blanusa snark.svg|[[Blanuša snarks|Blanuša snark (second)]]
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| File:Double-star snark.svg|[[Double-star snark]]
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| File:Flower snarkv.svg|[[Flower snark]]
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| File:Loupekine 1.svg|Loupekine snark (first)
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| File:Loupekine 2.svg|Loupekine snark (second)
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| File:Szekeres-snark.svg|[[Szekeres snark]]
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| File:Tietze's graph.svg|[[Tietze graph]]
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| File:Watkins snark.svg|[[Watkins snark]]
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| </gallery>
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| </center>
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| ===Star=== | |
| A [[star (graph theory)|star]] ''S''<sub>k</sub> is the [[complete bipartite graph]] ''K''<sub>1,''k''</sub>. The star ''S''<sub>3</sub> is called the claw graph.
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| [[File:Star graphs.svg|thumb|500px|center|The star graphs ''S''<sub>3</sub>, ''S''<sub>4</sub>, ''S''<sub>5</sub> and ''S''<sub>6</sub>.]]
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| ===Wheel graphs===
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| The [[wheel graph]] ''W<sub>n</sub>'' is a graph on ''n'' vertices constructed by connecting a single vertex to every vertex in an (''n'' − 1)-cycle.
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| [[File:Wheel graphs.svg|thumb|320px|center|Wheels <math>W_4</math> – <math>W_9</math>.]]
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| == References ==
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| {{reflist}}
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| {{DEFAULTSORT:Gallery Of Named Graphs}}
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| [[Category:Graphs|Named Graphs]]
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| [[Category:Graph families|Named Graphs]]
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