Construction of L-equienergetic graphs using some graph operations. Issue 3 (1st September 2020) - Vaidya, S. K.; Popat, Kalpesh M.
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 L ( G ) = D ( G ) − A ( G ) where D ( G ) is the diagonal matrix with ( i, j ) t h entry is the degree of vertex vi . The collection of eigenvalues of L ( G ) with their multiplicities is called spectra of L ( G ). If μ 1, μ 2, ⋯, μ n are the eigenvalues of L ( G ) then the Laplacian energy LE ( G ) of G is defined as L E ( G ) = ∑ i = 1 n | μ i − 2 m n | . 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.