Laplacian Sum-Eccentricity Energy of a Graph

Document Type: Special Issue: Energy of Graphs

Authors

1 Mysore University, Mysore, India

2 University Kragujevac, Serbia

Abstract

We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G,
and its Laplacian sum-eccentricity energy LS_eE=\sum_{i=1}^n |\eta_i|,
where \eta_i=\zeta_i-\frac{2m}{n} and where \zeta_1,\zeta_2,\ldots,\zeta_n
are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained.
A graph is said to be twinenergetic if \sum_{i=1}^n |\eta_i|=\sum_{i=1}^n |\zeta_i|.
Conditions for the existence of such graphs are established.

Keywords

Main Subjects


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