Seidel Signless Laplacian Energy of Graphs

Document Type : Special Issue: Energy of Graphs


1 Karnatak University

2 University Kragujevac, Serbia

3 Hirasugar Institute of Technology


Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,\ldots, n-1-2d_n)$ 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 $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+}(G)$ 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 $E_{SL^+}(G)$.


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