Energy and skew-energy of a modified graph

Graph energies draw the greater attention of the scientific community due to their direct applicability in molecular chemistry. In this paper, we establish the energy of a graph obtained by the means of some graph operations. The energy of the product of graph Kn × G, where Kn is a complete graph and G is a simple undirected graph and energy of the corresponding digraph are estimated. Further, the duplication graph DG is considered and proved that the energy E(DG) = 2E(G) and E(DGσ) = 2E(Gσ).

A Note on Skew Energy of Hadamard Graph

The skew spectrum and skew energy of an oriented graph are respectively the set of eigenvalues of the adjacency matrix of and the sum of the absolute values of the eigen values of the adjacency matrix of . In this work, we find and study the skew spectrum and the skew energy of Hadamard graph for a particular orientation.