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A nonreflexible regular map of genus 7 with eight graph vertices, 28 graph edges, and eight heptagonal faces.

Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

The Randić energy of a graph is defined as the graph energy of its Randić matrix, i.e., the sum of the absolute values of the eigenvalues of its Randić matrix.

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

The sequence of graphs starting with the Suzuki graph and successively taking local graphs, summarized in the following table, is known as the Suzuki tower, a name due to ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

The Petersen family of graphs, not to be confused with generalized Petersen graphs, are a set of seven graphs obtained from the Petersen graph (or complete graph K_6) by del ...