We show that, contrary to the claims of several authors that there exists no equienergetic graphs on seven vertices, there exists 21 sets of noncospectral, equienergetic graphs on seven vertices. We also give the number and cardinality of sets of equienergetic connected graphs on eight, nine and ten vertices, and equienergetic trees and chemical trees on up to 22 vertices. Finally, we construct...

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....

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 graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...

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 =...

The ISI-energy εisi(G) of a graph G=(V,E) is the sum absolute values eigenvalues ISI-matrix C(G)=[cij]n×n in which cij=d(vi)d(vj)d(vi)+d(vj) if vivj∈E(G) and cij=0 otherwise. d(vi) denotes degree vertex vi∈V. As class energy, can be utilized to ascertain general energy conjugated carbon molecules. Two non-isomorphic graphs same order are said ISI-equienergetic their ISI-energies equal. In this ...

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...