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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (4): 92-101.doi: 10.6040/j.issn.1671-9352.0.2024.330

• • 上一篇    

运算图的电阻距离和基尔霍夫指数

申云瑞,梅银珍*   

  1. 中北大学数学学院, 山西 太原 030051
  • 发布日期:2026-04-08
  • 通讯作者: 梅银珍(1977— ),女,教授,博士,研究方向为组合数学及图论应用. E-mail:myzmath@nuc.edu.cn
  • 作者简介:申云瑞(1998— ),女,硕士研究生,研究方向为组合数学及图论应用. E-mail:S202308034@st.nuc.edu.cn*通信作者:梅银珍(1977— ),女,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:
    山西省回国留学人员科研基金资助项目(2022-149);山西省基础研究计划基金资助项目(202303021211154)

Resistance distance and Kirchhoff index in graph operation

SHEN Yunrui, MEI Yinzhen*   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2026-04-08

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摘要： 设G为无向连通图,ST(G)、ZT(G)和HT(G)是G的运算图。利用电网络原理和组合方法,得到ST(G)、ZT(G)和HT(G)的基尔霍夫指数以及运算图的基尔霍夫指数与G的基尔霍夫指数、度积与度和基尔霍夫指数、边数、顶点数之间的关系。

关键词: 电阻距离, 基尔霍夫指数, 度积基尔霍夫指数, 度和基尔霍夫指数

Abstract: Let G be an undirected connected graph, ST(G),ZT(G),HT(G)are the operation graphs of G. By utilizing the principles of electrical networks and combinatorial methods, the Kirchhoff indices of ST(G),ZT(G),HT(G) are obtained, as well as the relationships between the Kirchhoff indices of graph operations and the Kirchhoff index of G, multiplicative degree-Kirchhoff index, additive degree-Kirchhoff index, the number of edges, and the number of vertices.

Key words: resistance distance, Kirchhoff index, multiplicative degree-Kirchhoff index, additive degree-Kirchhoff index

中图分类号: 

  • O157
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