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Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

A node in a graph for which the graph eccentricity equals the graph diameter (Harary 1994, p. 41).

The gyrobifastigium is an octahedron with on 8 vertices, 14 edges, and 8 faces. The equilateral gyrobifastigium is Johnson solid J_(26), consisting of two triangular prisms ...

The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

Graph Strength

A heptahedron is a polyhedron with seven faces. Because there are 34 heptahedral graphs, there are 34 topologically distinct convex heptahedra. There are three semiregular ...

In a graph G, two graph vertices are adjacent if they are joined by a graph edge.

A graph vertex in a graph is said to be an even node if its vertex degree is even.