Non-self-centrality in the corona product of graphs

Abstract

The non-self-centrality number (NSC number for short) of a graph G is a novel graph invariant defined as follows: = I 'fi where the summation goes over all the unordered pairs of vertices in G and e. is the eccentricity of vertex vt in G. The third Zagreb eccentricity index of a graph G is also a novel graph invariant defined as f3 ( G) = ev Ey(G) is a good indicator for the non-self-centrality of a graph whereas yV( G) is defined for better indicating the non-self-centrality of a graph. In this paper, explicit formulae are presented and algorithms that have polynomial time complexity are proposed for computing those eccentricity-related invariants for composite graphs. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.