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A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

A permutation group (G,X) is k-homogeneous if it is transitive on unordered k-subsets of X. The projective special linear group PSL(2,q) is 3-homogeneous if q=3 (mod 4).

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

The triangular graph T_n=L(K_n) is the line graph of the complete graph K_n (Brualdi and Ryser 1991, p. 152). The vertices of T_n may be identified with the 2-subsets of ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

A notion introduced by R. M. Wilson in 1974. Given a finite graph G with n vertices, puz(G) is defined as the graph whose nodes are the labelings of G leaving one node ...

Consider a star graph S_(n+1) consisting of a central hub vertex and n spokes, but instead of placing a single point at the end of each spoke, place k points along it (in ...

A graph cycle.

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...