TY - JOUR
ID - 113761
TI - On Eccentric Adjacency Index of Graphs and Trees
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Sharafdini, Reza
AU - Azadimotlagh, Mehdi
AU - Hashemi, Vahid
AU - Parsanejad, Fateme
AD - Persian Gulf University
AD - Department of Computer Engineering of Jam, Persian Gulf University, Jam, IRAN
AD - Faculty of intelligent systems engineering and data science,
Persian Gulf University, Bushehr 75169.
Y1 - 2023
PY - 2023
VL - 8
IS - 1
SP - 1
EP - 17
KW - Eccentricity
KW - tree
KW - eccentric adjacency index (EAI)
KW - perfect matching
DO - 10.22052/mir.2023.246384.1391
N2 - 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.
UR - https://mir.kashanu.ac.ir/article_113761.html
L1 - https://mir.kashanu.ac.ir/article_113761_25bbe911758dc04c41038b96ac151cd4.pdf
ER -