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simple graphs with five vertices. One of them is the butterfly graph. The two others are cycle graph
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The full automorphism group of the butterfly graph is a group of order 8 isomorphic to the
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544:, Lecture Notes in Comput. Sci., vol. 4381, Springer, Berlin, pp. 10–20,
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are bowtie-free graphs, since every butterfly contains a triangle.
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ISGCI: Information System on Graph
Classes and their Inclusions. "
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and 6 edges. It can be constructed by joining 2 copies of the
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542:Discrete geometry, combinatorics and graph theory
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536:Ando, Kiyoshi (2007), "Contractible edges in a
364:, including both rotations and reflections.
449:{\displaystyle -(x-1)(x+1)^{2}(x^{2}-x-4)}
338:-vertex-connected bowtie-free graph has a
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201:with a common vertex and is therefore
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16:Planar graph with 5 nodes and 6 edges
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334:and Yoshimoto proved that every
330:-connected graph. Ando, Kaneko,
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360:, the group of symmetries of a
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150:Table of graphs and parameters
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318:graph, an edge is said to be
300:if it has no butterfly as an
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550:10.1007/978-3-540-70666-3_2
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371:of the butterfly graph is
369:characteristic polynomial
244:(this implies that it is
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220:The butterfly graph has
324:contraction of the edge
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254:vertex-connected graph
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322:-contractible if the
263:There are only three
499:List of Small Graphs
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346:Algebraic properties
342:-contractible edge.
306:triangle-free graphs
258:edge-connected graph
236: 4 and is both
540:-connected graph",
228: 3, radius 1,
513:Weisstein, Eric W.
475:Weisstein, Eric W.
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292:Bowtie-free graphs
252:). It is also a 1-
578:Individual graphs
478:"Butterfly Graph"
316:-vertex-connected
169:(also called the
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516:"Graceful graph"
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302:induced subgraph
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230:chromatic number
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207:friendship graph
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183:undirected graph
108:Chromatic number
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234:chromatic index
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118:Chromatic index
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265:non-graceful
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224: 2 and
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171:bowtie graph
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163:graph theory
159:mathematical
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143:Not graceful
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298:bowtie-free
296:A graph is
242:penny graph
191:cycle graph
572:Categories
460:References
203:isomorphic
127:Properties
521:MathWorld
483:MathWorld
438:−
432:−
388:−
379:−
232: 3,
161:field of
276:and the
256:and a 2-
238:Eulerian
222:diameter
187:vertices
173:and the
139:Eulerian
67:Diameter
37:Vertices
558:2364744
205:to the
185:with 5
177:) is a
157:In the
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362:square
304:. The
250:planar
240:and a
179:planar
165:, the
131:Planar
57:Radius
311:In a
226:girth
77:Girth
47:Edges
367:The
248:and
546:doi
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