Eccentric Connectivity Index of Strongly Connected Digraphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912596937932800 |
|---|---|
| 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 |