Maximum Zagreb Indices Among All $p-$Quasi $k-$Cyclic Graphs

	Maximum Zagreb Indices Among All $p-$Quasi $k-$Cyclic Graphs
Journal of Algorithms and Computation
مقاله 7، دوره 51، شماره 2، اسفند 2019، صفحه 75-82 اصل مقاله (269.96 K)
شناسه دیجیتال (DOI): 10.22059/jac.2019.75164
نویسندگان
Ali Reza Ashrafi^* ؛ Ali Ghalavand
University of Kashan
چکیده
\vspace{0.2cm} Suppose $G$ is a simple and connected graph. The first and second Zagreb indices of $G$ are two degree-based graph invariants defined as $M_1(G) = \sum_{v \in V(G)}deg(v)^2$ and $M_2(G) = \sum_{e=uv \in E(G)}deg(u)deg(v)$, respectively. The graph $G$ is called $p-$quasi $k-$cyclic, if there exists a subset $S$ of vertices such that $\|S\| = p$, $G \setminus S$ is $k-$cyclic and there is no a subset $S^\prime$ of $V(G)$ such that $\|S^\prime\| < \|S\|$ and $G \setminus S^\prime$ is $k-$cyclic. The aim of this paper is to characterize all graphs with maximum values of Zagreb indices among all $p-$quasi $k-$cyclic graphs with $k \leq 3$. & & \vspace{0.2cm}
کلیدواژه‌ها
$p-$quasi $k-$cyclic graph؛ first Zagreb index؛ second Zagreb index؛ cyclomatic number؛ k-cyclic graph

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