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On digraphs with maximum first outdegree Zagreb index | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آبان 1404 اصل مقاله (593.07 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30676.2573 | ||
| نویسندگان | ||
| Hilal A. Ganie1؛ Shariefuddin Pirzada* 2 | ||
| 1Department of Mathematics, Government Degree College Uri, Kashmir, India | ||
| 2Department of Mathematics, University of Kashmir, India | ||
| چکیده | ||
| Let $D$ be a digraph with order $n$ and $a$ arcs. Let $d_1^{+}, d_2^{+},\dots, d_n^{+}$ be the vertex outdegrees of $D$. The first outdegree Zagreb index of $D$ is denoted by $Zg^{+}(D)$ and is defined as $Zg^{+}D)=\sum\limits_{i=1}^{n}(d_i^{+})^2$. In this paper, we completely characterize the oriented graphs which attain the maximum value for the first outdegree Zagreb index $Zg^{+}(D)$ among all connected oriented graphs $D$ of order $n$ with $n-1\le a\le 2n-3$. Further, we determine the oriented graphs which attain the second maximum value for $Zg^{+}(D)$ among all oriented graphs of order $n$ with $n-1\le a\le n+2$. We consider the problem of determining the orientations which attain the maximum and the minimum values for the first outdegree Zagreb index for the Path, the Cycle and the Star. | ||
| کلیدواژه‌ها | ||
| digraph؛ oriented graph؛ topological index؛ first outdegree Zagreb index | ||
| مراجع | ||
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