The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two graphs are equienergetic if they have the same energy. We construct infinite families of graphs equienergetic with edge-deleted subgraphs.

The energy of a simple graph G is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two graphs of the same order are said to be equienergetic if they have the same energy. Several ways to construct equienergetic non-cospectral graphs of very large size can be found in the literature. The aim of this work is to construct equienergetic non-cospectral graphs of small size....

For a simple digraph G of order n with vertex set {v1, v2, . . . , vn}, let d+i and d − i denote the out-degree and in-degree of a vertex vi in G, respectively. Let D (G) = diag(d+1 , d + 2 , . . . , d + n ) and D−(G) = diag(d1 , d − 2 , . . . , d − n ). In this paper we introduce S̃L(G) = D̃(G)−S(G) to be a new kind of skew Laplacian matrix of G, where D̃(G) = D+(G)−D−(G) and S(G) is the skew-adj...

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D , and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p =...

Given a digraph D, the set of all pairs (N−(v), N(v)) constitutes the neighborhood dihypergraph N (D) of D. The Digraph Realization Problem asks whether a given dihypergraph H coincides with N (D) for some digraph D. This problem was introduced by Aigner and Triesch [2] as a natural generalization of the Open Neighborhood Realization Problem for undirected graphs, which is known to be NP-comple...

The D-eigenvalues of a connected graph G are the eigenvalues of its distance matrix D, and form the D-spectrum of G. The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two (connected) graphs are said to be D-equienergetic if they have equal D-energies. The D-spectra of some graphs and their D-energies are calculated. A pair of D-equienergetic bipartite gra...