On Sombor index of extremal graphs

Rouhani, Soheir; Habibi, Mohammad; Mehrpouya, Mohammad Ali

doi:10.22061/jdma.2024.11328.1101

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	On Sombor index of extremal graphs
Journal of Discrete Mathematics and Its Applications
دوره 9، شماره 4، اسفند 2024، صفحه 335-344 اصل مقاله (491.56 K)
نوع مقاله: Full Length Article
شناسه دیجیتال (DOI): 10.22061/jdma.2024.11328.1101
نویسندگان
Soheir Rouhani¹؛ Mohammad Habibi^* ²؛ Mohammad Ali Mehrpouya³
¹Department of Mathematics Tafresh University Tafresh
²Tafresh University
³Department of Mathematics Tafresh University Tafresh
تاریخ دریافت: 13 مهر 1403، تاریخ بازنگری: 17 مهر 1403، تاریخ پذیرش: 22 آبان 1403
چکیده
Let $ G $ be a finite simple graph. The Sombor index of $ G $ is defined as $ \sum\nolimits_{uv\in E(G)} \sqrt{d_{u}^{2}+d_{v}^{2}} $ where $d_{u}$ and $d_{v}$ represent the degrees of vertices $ u$ and $v$ in $ G $, respectively. The sum of the absolute values of the adjacency eigenvalues defines the energy of a graph. This paper aims to enhance the current connections between the Sombor index and the energy of graphs. Additionally, we provide some upper bounds for the Sombor index of triangle-free, square-free, $K_r$-free and tripartite graphs in terms of order, size and minimum degree.
کلیدواژه‌ها
$C_4$-free graph؛ energy؛ Sombor index؛ tripartite graph؛ triangle-free graph

مراجع
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On Sombor index of extremal graphs