Seidel Signless Laplacian Energy of Graphs

نویسندگان
Ramane, Harishchandra S. ID 1
Jummannaver, Raju B. ID 2
Gutman, Ivan ID 3
Patil, Jayashri B. ID 4

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

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

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

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

doi
10.22052/mir.2017.101641.1081
چکیده

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).

کلیدواژه‌ها
Seidel Laplacian eigenvalues, Seidel Laplacian energy, Seidel signless Laplacian matrix, Seidel signless Laplacian eigenvalues, Seidel signless Laplacian energy