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General Randić index of unicyclic graphs with given maximum degree | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 اردیبهشت 1404 اصل مقاله (423.76 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30340.2425 | ||
| نویسندگان | ||
| Elize Swartz؛ Tomáš Vetrík* | ||
| Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa | ||
| چکیده | ||
| The general Randi'{c} index of a graph $G$ is defined as $R_{a} (G) = \sum_{uv \in E(G)} [d_G (u) d_G (v)]^{a}$, where $a \in \mathbb{R}$, $E(G)$ is the set of edges of $G$, and $d_G (u)$ and $d_G (v)$ are the degrees of vertices $u$ and $v$, respectively. Among unicyclic graphs with given number of vertices and maximum degree, we present the graph with the largest value of $R_{a}$ for $a < 0$, and graphs having the smallest values of $R_{a}$ for $a > 0$. | ||
| کلیدواژهها | ||
| extremal graph؛ topological index؛ cycle | ||
| مراجع | ||
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