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Butterfly graph

"The" butterfly graph is a name sometimes given to the 5-vertex graph illustrated above. This graph is also known as the "bowtie graph" (West 2000, p. 12) and is the triangular snake graph . The butterfly graph is ungraceful (Horton 2003). It is implemented in the Wolfram Language as GraphData["ButterflyGraph"].A different type of butterfly graph is defined as follows. The -dimensional butterfly graph is a directed graph whose vertices are pairs , where is a binary string of length and is an integer in the range 0 to and with directed edges from vertex to iff is identical to in all bits with the possible exception of the th bit counted from the left.The -dimensional butterfly graph has vertices and edges, and can be generated in the Wolfram Language using ButterflyGraph[n, b] (with )...

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