Eccentric Connectivity Index of Cartesian product and Strong product of Strongly Connected Digraphs
Abstract
Let G=(V,E) be a graph. The \emph{eccentric connectivity index} of G is defined as ξC(G)=∑u∈ V(G)duecc(u) where du and ecc(u) are the degree and eccentricity of u, respectively. For a strongly connected digraph D=(V,A), the eccentric connectivity index is defined as ξC(D)=1/2∑u∈ V(D)(du++du-)mecc(u) where du+ and du- are the out-degree and in-degree of u, respectively, and mecc(u) is its m-eccentricity with respect to the maximum distance md(u,v)=max{d⃗(u,v),d⃗(v,u)}. In this article, give formulas and bounds for the eccentric connectivity index of Cartesian and strong products of strongly connected digraphs and discuss the corresponding equality cases. Also, an attempt is made to study the self-centeredness of these products and establish conditions under which the Cartesian and strong products are self-centered.The results are extended to products of several digraphs.
Related
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BibTeX
@misc{chakooth2026eccentric,
title = {{Eccentric Connectivity Index of Cartesian product and Strong product of Strongly Connected Digraphs}},
author = {Vysakh Chakooth and Prasanth G. Narasimha-Shenoi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13772},
eprint = {2609.13772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13772},
}
RIS
TY - UNPB
TI - Eccentric Connectivity Index of Cartesian product and Strong product of Strongly Connected Digraphs
AU - Vysakh Chakooth
AU - Prasanth G. Narasimha-Shenoi
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13772
UR - https://arxiv.org/abs/2609.13772
AB - Let G=(V,E) be a graph. The \emph{eccentric connectivity index} of G is defined as ξ^C(G)=∑_u∈ V(G)d_uecc(u) where d_u and ecc(u) are the degree and eccentricity of u, respectively. For a strongly connected digraph D=(V,A), the eccentric connectivity index is defined as ξ^C(D)=1/2∑_u∈ V(D)(d_u^++d_u^-)mecc(u) where d_u^+ and d_u^- are the out-degree and in-degree of u, respectively, and mecc(u) is its m-eccentricity with respect to the maximum distance md(u,v)=max{d⃗(u,v),d⃗(v,u)}. In this article, give formulas and bounds for the eccentric connectivity index of Cartesian and strong products of strongly connected digraphs and discuss the corresponding equality cases. Also, an attempt is made to study the self-centeredness of these products and establish conditions under which the Cartesian and strong products are self-centered.The results are extended to products of several digraphs.
ER -