运算图的电阻距离和基尔霍夫指数

Resistance distance and Kirchhoff index in graph operation

摘要

设G为无向连通图,S _T(G)、Z _T(G)和H _T(G)是G的运算图。利用电网络原理和组合方法,得到S _T(G)、Z _T(G)和H _T(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。

Abstract

Let G be an undirected connected graph, S _T(G), Z _T(G), H _T(G) are the operation graphs of G. By utilizing the principles of electrical networks and combinatorial methods, the Kirchhoff indices of S _T(G), Z _T(G), H _T(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.

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

Key words

resistance distance / Kirchhoff index / multiplicative degree-Kirchhoff index / additive degree-Kirchhoff index

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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)