On the first and second Zagreb indices of quasi unicyclic graphs
Publish place: Transactions on Combinatorics، Vol: 8، Issue: 3
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_COMB-8-3_005
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
Let $G$ be a simple graph. The graph $G$ is called a quasi unicyclic graph if there exists a vertex $x \in V(G)$ such that $G-x$ is a connected graph with a unique cycle. Moreover, the first and the second Zagreb indices of $G$ denoted by $M_۱(G)$ and $M_۲(G)$, are the sum of $\deg^۲(u)$ overall vertices $u$ in $G$ and the sum of $\deg(u)\deg(v)$ of all edges $uv$ of $G$, respectively. The first and the second Zagreb indices are defined relative to the degree of vertices. In this paper, sharp upper and lower bounds for the first and the second Zagreb indices of quasi unicyclic graphs are given.
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Authors
Majid Aghel
Ferdowsi University of Mashhad, International Campus
Ahmad Erfanian
Ferdowsi University
Ali Reza Ashrafi
University of Kashan