Eccentric connectivity index and eccentric distance sum of some graph operations

Document Type: Research Paper

Authors

1 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R. China

2 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Abstract

Let $G=(V,E)$ be a connected graph‎. ‎The eccentric connectivity index of $G$‎, ‎$\xi^{c}(G)$‎, ‎is defined as‎
‎$\xi^{c}(G)=\sum_{v\in V(G)}deg(v)ec(v)$‎, ‎where $deg(v)$ is the‎ ‎degree of a vertex $v$ and $ec(v)$ is its eccentricity‎. ‎The‎ ‎eccentric distance sum of $G$ is defined as $\xi^{d}(G)=\sum_{v\in‎ ‎V(G)}ec(v)D(v)$‎, ‎where $D(v)=\sum_{u\in V(G)}d(u,v)$‎. ‎In this paper‎, ‎we calculate the eccentric connectivity index and eccentric distance‎ ‎sum of generalized hierarchical product of graphs‎. ‎Moreover‎, ‎we‎ ‎present the exact formulae for the eccentric connectivity index of‎ ‎$F$-sum graphs in terms of some invariants of the factors‎.

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Main Subjects


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