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An (n,k)-firecracker is a graph obtained by the concatenation of n k-stars by linking one leaf from each (Chen et al. 1997, Gallian 2007). Firecracker graphs are graceful ...

The gem graph is the fan graph F_(4,1) illustrated above. It is implemented in the Wolfram Language as GraphData["GemGraph"].

The Hoffman graph is the bipartite graph on 16 nodes and 32 edges illustrated above that is cospectral to the tesseract graph Q_4 (Hoffman 1963, van Dam and Haemers 2003). ...

Knuth (2008, p. 44) terms the 24-vertex graph based on the notes of the musical scale illustrated above the "musical graph." This graph can be seen to be the 24-vertex case ...

The triangular snake graph TS_n is the graph on n vertices with n odd defined by starting with the path graph P_(n-1) and adding edges (2i-1,2i+1) for i=1, ..., n-1. The ...

The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. ...

The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance to a schematic illustration of a house ...

The Szekeres snark was the fifth snark discovered, illustrated above. It has 50 vertices and edge chromatic number 4.

The Watkins snark is the snark on 50 vertices ad 75 nodes illustrated above. It is implemented in the Wolfram Language as GraphData["WatkinsSnark"].

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...