Seidel Signless Laplacian Energy of Graphs

Document Type : Special Issue: Energy of Graphs


1 Department of Mathematics, Karnatak University, Dharwad – 580003, India

2 Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia

3 Department of Mathematics, Hirasugar Institute of Technology, Nidasoshi – 591236, India


Let S(G) be the Seidel matrix of a graph G of order n and let DS(G)=diag(n-1-2d1, n-1-2d2,..., n-1-2dn) be the diagonal matrix with d_i denoting the degree of a vertex v_i in G. The Seidel Laplacian matrix of G is defined as SL(G)=D_S(G)-S(G) and the Seidel signless Laplacian matrix as SL+(G)=DS(G)+S(G). The Seidel signless Laplacian energy ESL+(G) is defined as the sum of the absolute deviations of the eigenvalues of SL+(G) from their mean. In this paper, we establish the main properties of the eigenvalues of SL+(G) and of ESL+(G).


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