Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications

The eccentric-distance sum of some graphs

Padmapriya P (Department of Studies in Mathematics University of Mysore, Manasagangotri Mysuru - 570 006, India)
Veena Mathad (Department of Studies in Mathematics University of Mysore, Manasagangotri Mysuru - 570 006, India)

Article Info

Publish Date
10 Apr 2017

Abstract

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.

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Journal Info
Electronic Journal of Graph Theory and Applications (EJGTA)
Website

Abbrev

ejgta

Publisher

Indonesian Combinatorial Society

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...