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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (6): 56-63.doi: 10.6040/j.issn.1671-9352.0.2023.042

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四类运算图的Sombor指数

梅银珍(),符惠芬   

  1. 中北大学数学学院, 山西 太原 030051
  • 收稿日期:2023-02-06 出版日期:2024-06-20 发布日期:2024-06-17
  • 作者简介:梅银珍(1977—), 女, 副教授, 博士, 研究方向为组合数学及图论应用. E-mail: myzmath@nuc.edu.cn
  • 基金资助:
    国家自然科学基金项目资助项目(61774137);山西省回国留学人员科研项目(2022-149);山西省基础研究计划资助项目(20210302124212)

Sombor index on four operation graphs

Yinzhen MEI(),Huifeng FU   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Received:2023-02-06 Online:2024-06-20 Published:2024-06-17

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摘要：

设图G是一个简单图, E(G)为G的边集, du, dv分别为顶点u, v的度.本文在图的S(G)、R(G)、Q(G)、T(G)4种变换运算和两图的笛卡尔积相结合的F-和定义基础上, 利用最大度, 通过分类讨论的方法, 计算了四种相关运算图的Sombor指数的上界, 并且刻画了相应的极值。

关键词: Sombor指数, 图运算, 笛卡尔积, F-和

Abstract:

Let G be a simple graph, E(G) be the edge set of G, and, du, dv be the degree of vertex u, v, respectively. In this paper, we focuse on the definition of F- sum of graphs combined with four transformation operations S(G), R(G), Q(G), T(G) and Cartesian product of two graphs, and calculate the upper bound of the Sombor index of the four kinds of related graphs by using the maximum degree and classification, and characterize their extreme values.

Key words: sombor index, graph operations, cartesian product, F-sum

中图分类号: 

  • O157.5

图1

S(P5), R(P5), Q(P5), T(P5)示例图"

图2

G+FH示例图"

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