在仙人掌的末端有最小的Sombor指数

IF 1.8 3区 数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.20231537
Qiaozhi Geng, Shengjie He, Rong-Xia Hao
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引用次数: 0

摘要

&lt;abstract&gt;&lt; &gt;设$ H $为边集$ E_H $的图。定义图$ H $的Sombor指数和约简Sombor指数分别为$ SO(H) = \sum\limits_{uv\in E_H}\sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $和$ SO_{red}(H) = \sum\limits_{uv\in E_H}\sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $。其中$ d_{H}(u) $和$ d_{H}(v) $分别是$ H $中顶点$ u $和$ v $的度数。仙人掌是一个连通图,其中任意两个环最多有一个公共顶点。设$ \mathcal{C}(n, k) $为次为$ n $的仙人掌类,周期为$ k $。本文得到了$ \mathcal{C}(n, k) $中仙人掌Sombor指数的下界,并在$ n\geq 4k-2 $和$ k\geq 2 $中对对应的仙人掌极值进行了表征。此外,用类似的方法得到了仙人掌的Sombor指数的下界。&lt;/ &lt;/abstract&gt;
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On the extremal cacti with minimum Sombor index

Let $ H $ be a graph with edge set $ E_H $. The Sombor index and the reduced Sombor index of a graph $ H $ are defined as $ SO(H) = \sum\limits_{uv\in E_H}\sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $ and $ SO_{red}(H) = \sum\limits_{uv\in E_H}\sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $, respectively. Where $ d_{H}(u) $ and $ d_{H}(v) $ are the degrees of the vertices $ u $ and $ v $ in $ H $, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $ \mathcal{C}(n, k) $ be the class of cacti of order $ n $ with $ k $ cycles. In this paper, the lower bound for the Sombor index of the cacti in $ \mathcal{C}(n, k) $ is obtained and the corresponding extremal cacti are characterized when $ n\geq 4k-2 $ and $ k\geq 2 $. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach.

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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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