The lower bound of revised edge-Szeged index of unicyclic graphs with given diameter

doi:10.3868/s140-DDD-023-0020-x

Frontiers of Mathematics in China

2023, Vol. 18

Issue (4): 251-275 https://doi.org/10.3868/s140-DDD-023-0020-x

本期目录

The lower bound of revised edge-Szeged index of unicyclic graphs with given diameter

Min WANG, Mengmeng LIU(

)

Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730000, China

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Abstract：

Given a connected graph $G$ , the revised edge-revised Szeged index is defined as $S z e ∗ (G) = ∑ e = u v ∈ E G (m u (e) + m 0 (e) 2) (m v (e) + m 0 (e) 2)$ , where $m u (e)$ , $m v (e)$ and $m 0 (e)$ are the number of edges of $G$ lying closer to vertex $u$ than to vertex $v$ , the number of edges of $G$ lying closer to vertex $v$ than to vertex $u$ and the number of edges of $G$ at the same distance to $u$ and $v$ , respectively. In this paper, by transformation and calculation, the lower bound of revised edge-Szeged index of unicyclic graphs with given diameter is obtained, and the extremal graph is depicted.

Key words： Wiener index revised edge Szeged index unicyclic graph extremal graph

出版日期: 2023-12-12

Corresponding Author(s): Mengmeng LIU

引用本文:

. [J]. Frontiers of Mathematics in China, 2023, 18(4): 251-275.
Min WANG, Mengmeng LIU. The lower bound of revised edge-Szeged index of unicyclic graphs with given diameter. Front. Math. China, 2023, 18(4): 251-275.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.3868/s140-DDD-023-0020-x
https://academic.hep.com.cn/fmc/CN/Y2023/V18/I4/251

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