Extremal spectral radius of degree-based weighted adjacency matrices of graphs with given order and size

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-11-07 DOI:10.1016/j.dam.2024.10.025

Chenghao Shen, Haiying Shan

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引用次数: 0

Abstract

The

f

-adjacency matrix is a type of edge-weighted adjacency matrix, whose weight of an edge

i j

f (d_{i}, d_{j})

, where

f

is a real symmetric function and

d_{i}, d_{j}

are the degrees of vertex

i

and vertex

j

. The

f

-spectral radius of a graph is the spectral radius of its

f

-adjacency matrix. In this paper, the effect of subdividing an edge on

f

-spectral radius is discussed. Some necessary conditions of the extremal graph with given order and size are derived. As an application of these results, we obtain the bicyclic graph(s) with the smallest

f

-spectral radius for fixed order

n \geq 8

by applying generalized Lu–Man method.

查看原文本刊更多论文

给定阶数和大小的图的基于度的加权邻接矩阵的极谱半径

f-adjacency 矩阵是一种边缘加权邻接矩阵，其边缘 ij 的权重为 f(di,dj)，其中 f 是实对称函数，di,dj 是顶点 i 和顶点 j 的度数。本文讨论了细分边对 f 谱半径的影响。本文推导了具有给定阶数和大小的极值图的一些必要条件。作为这些结果的应用，我们应用广义鲁曼法得到了固定阶数 n≥8 时 f 谱半径最小的双环图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.