Eccentric Connectivity Index of Strongly Connected Digraphs

Fuente: arXiv
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Autores principales: Chakooth, Vysakh, Narasimha-Shenoi, Prasanth G., Narasimha-Shenoi, Prakash G.
Formato: Preprint
Publicado: 2025
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author Chakooth, Vysakh
Narasimha-Shenoi, Prasanth G.
Narasimha-Shenoi, Prakash G.
author_facet Chakooth, Vysakh
Narasimha-Shenoi, Prasanth G.
Narasimha-Shenoi, Prakash G.
contents Let $G = (V, E)$ be a graph with non-empty set of vertices $V$ and set of edges $E$. The \emph{eccentric connectivity index} of the graph $G$ is defined as $$\displaystyle{ξ^C(G) = \sum_{u \in V} d_u \;ecc(u)}$$ where $d_u$ is the degree and $ecc(u)$ is the eccentricity of the vertex $u \in V$. This article is an attempt to find the \emph{eccentric connectivity index} of strongly connected digraph $D$ with respect to the metric, \textit{maximum distance} defined by $md(u,v)=\max\{\vec{d}(u,v),\vec{d}(v,u)\}$. An attempt is also made to find the extremal values for strongly connected digraphs.
format Preprint
id arxiv_https___arxiv_org_abs_2509_17019
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Eccentric Connectivity Index of Strongly Connected Digraphs
Chakooth, Vysakh
Narasimha-Shenoi, Prasanth G.
Narasimha-Shenoi, Prakash G.
Combinatorics
Discrete Mathematics
05C12, 05C35, 05C90
Let $G = (V, E)$ be a graph with non-empty set of vertices $V$ and set of edges $E$. The \emph{eccentric connectivity index} of the graph $G$ is defined as $$\displaystyle{ξ^C(G) = \sum_{u \in V} d_u \;ecc(u)}$$ where $d_u$ is the degree and $ecc(u)$ is the eccentricity of the vertex $u \in V$. This article is an attempt to find the \emph{eccentric connectivity index} of strongly connected digraph $D$ with respect to the metric, \textit{maximum distance} defined by $md(u,v)=\max\{\vec{d}(u,v),\vec{d}(v,u)\}$. An attempt is also made to find the extremal values for strongly connected digraphs.
title Eccentric Connectivity Index of Strongly Connected Digraphs
topic Combinatorics
Discrete Mathematics
05C12, 05C35, 05C90
url https://arxiv.org/abs/2509.17019