Laplacian Sum-Eccentricity Energy of a Graph

Document Type : Special Issue: Energy of Graphs


1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru – 570 006, India

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


We introduce the Laplacian sum-eccentricity matrix LSe of a graph G, and its Laplacian sum-eccentricity energy LSeE=∑ni=1i|, where ηii-(2m/n) and where ξ12,...,ξn are the eigenvalues of LSe. Upper bounds for LSeE are obtained. A graph is said to be twinenergetic if ∑ni=1i|=∑ni=1i|. Conditions for the existence of such graphs are established.


Main Subjects

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