University of Kashan Mathematics Interdisciplinary Research 2538-3639 2 2 2017 12 01 Laplacian Sum-Eccentricity Energy of a Graph 209 219 54000 10.22052/mir.2017.106176.1084 EN Biligirirangaiah Sharada Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru – 570 006, India Mohammad Issa Sowaity Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru – 570 006, India Ivan Gutman Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia Journal Article 2017 11 19 We introduce the Laplacian sum-eccentricity matrix <strong>LS<sub>e</sub></strong> of a graph G, and its Laplacian sum-eccentricity energy LS<sub>e</sub>E=∑<sup>n</sup><sub>i=1</sub>|η<sub>i</sub>|, where η<sub>i</sub>=ξ<sub>i</sub>-(2m/n) and where ξ<sub>1</sub>,ξ<sub>2</sub>,...,ξ<sub>n </sub>are the eigenvalues of <strong>LS<sub>e</sub></strong>. Upper bounds for LS<sub>e</sub>E are obtained. A graph is said to be twinenergetic if ∑<sup>n</sup><sub>i=1</sub>|η<sub>i</sub>|=∑<sup>n</sup><sub>i=1</sub>|ξ<sub>i</sub>|. Conditions for the existence of such graphs are established. Sum-eccentricity eigenvalues sum-eccentricity energy Laplacian sum-eccentricity matrix Laplacian sum-eccentricity energy https://mir.kashanu.ac.ir/article_54000_a60755aff16ea35f3f068051c0878426.pdf