@article {
author = {Sharafdini, Reza and Azadimotlagh, Mehdi and Hashemi, Vahid and Parsanejad, Fateme},
title = {On Eccentric Adjacency Index of Graphs and Trees},
journal = {Mathematics Interdisciplinary Research},
volume = {8},
number = {1},
pages = {1-17},
year = {2023},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2023.246384.1391},
abstract = {Let $G=(V(G),E(G))$ be a simple and connected graph. The distance between any two vertices $x$ and $y$, denoted by $d_G(x,y)$, is defined as the length of a shortest path connecting $x$ and $y$ in $G$.The degree of a vertex $x$ in $G$, denoted by $\deg_G(x)$, is defined as the number of vertices in $G$ of distance one from $x$.The eccentric adjacency index (briefly EAI) of a connected graph $G$ is defined as\[\xi^{ad} (G)=\sum_{u\in V(G)}\se_G(u)\varepsilon_G(u)^{-1},\]\noindentwhere $\se_G(u)=\displaystyle\sum_{\substack{v\in V(G)\\ d_G(u,v)=1}}\deg_{G}(v)$ and$\varepsilon_G(u)=\max \{d_G(u,v)\mid v \in V(G)\}$.In this article, we aim to obtain all extremal graphs based on the value ofEAI among all simple and connected graphs, all trees, and all trees with perfect matching.},
keywords = {Eccentricity,tree,eccentric adjacency index (EAI),perfect matching},
url = {https://mir.kashanu.ac.ir/article_113761.html},
eprint = {https://mir.kashanu.ac.ir/article_113761_25bbe911758dc04c41038b96ac151cd4.pdf}
}