The Energy and Operations of Graphs

Abstract

Let G be a finite and undirected simple graph on n vertices, A(G) is the adjacency matrix of G , λ 1 ,λ 2 ,...,λ n are eigenvalues of A(G) , then the energy of G is . In this paper, we determine the energy of graphs obtained from a graph by other unary operations, or graphs obtained from two graphs by other binary operations. In terms of binary operation, we prove that the energy of product graphs is equal to the product of the energy of graphs G 1 and G 2 , and give the computational formulas of the energy of Corona graph , join graph of two regular graphs G and H , respectively. In terms of unary operation, we give the computational formulas of the energy of the duplication graph D m G , the line graph L(G) , the subdivision graph S(G) , and the total graph T(G) of a regular graph G , respectively. In particularly, we obtained a lot of graphs pair of equienergetic.