Construction of L-equienergetic graphs using some graph operations

Abstract

For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as where D(G) is the diagonal matrix with entry is the degree of vertex vi. The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral.