University of KashanMathematics Interdisciplinary Research2538-36392220171201Seidel Signless Laplacian Energy of Graphs1811915399810.22052/mir.2017.101641.1081ENHarishchandra S.RamaneDepartment of Mathematics,
Karnatak University,
Dharwad – 580003, IndiaIvanGutmanFaculty of Science,
University of Kragujevac,
P.O. Box 60, 34000 Kragujevac, SerbiaJayashri B.PatilDepartment of Mathematics,
Hirasugar Institute of Technology,
Nidasoshi – 591236, IndiaRaju B.JummannaverDepartment of Mathematics,
Karnatak University,
Dharwad – 580003, IndiaJournal Article20171020Let S(G) be the Seidel matrix of a graph G of order n and let D<sub>S</sub>(G)=diag(n-1-2d<sub>1</sub>, n-1-2d<sub>2</sub>,..., n-1-2d<sub>n</sub>) 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<sup>+</sup>(G)=D<sub>S</sub>(G)+S(G). The Seidel signless Laplacian energy E<sub>SL+</sub>(G) is defined as the sum of the absolute deviations of the eigenvalues of SL<sup>+</sup>(G) from their mean. In this paper, we establish the main properties of the eigenvalues of SL<sup>+</sup>(G) and of E<sub>SL+</sub>(G).https://mir.kashanu.ac.ir/article_53998_01ab0ae77936bf1f5161db2349204526.pdf