University of KashanMathematics Interdisciplinary Research2538-36392220171201Seidel Signless Laplacian Energy of Graphs1811915399810.22052/mir.2017.101641.1081ENHarishchandra S.RamaneKarnatak UniversityIvanGutmanUniversity Kragujevac, SerbiaJayashri B.PatilHirasugar Institute of TechnologyRaju B.JummannaverKarnatak UniversityJournal Article20171020Let $S(G)$ 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<br /> with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian<br /> matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless<br /> 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 $E_{SL^+}(G)$.http://mir.kashanu.ac.ir/article_53998_01ab0ae77936bf1f5161db2349204526.pdf