e-Adjacency matrix and e-Laplacian matrix of semigraph

Abstract

In this paper we define e-Adjacency matrix A_e(S) and e-Laplacian matrix of a Semigraph L_e(S). Also discuss some results of eigenvalues of these matrices. We define e-Energy of Semigraph E_e(S) using eigenvalues of its e-adjacency matrix and e- Laplacian energy of Semigraph LE_e (S) using eigenvalues of its e-Laplacian matrix. We investigate relation between e-energy E_e(S) and e-Laplacian energy LE_e(S) for regular Semigraphs.