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The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

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 ...

"Conext 21 polyhedron" is the name given here to the solid underlying the soccer ball of the 2020 Tokyo Olympic Games (held in 2021). It is implemented in the Wolfram ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

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 ...