完全（2,2）二部图

IF 0.5 Q3 MATHEMATICS

Malaysian Journal of Mathematical Sciences Pub Date : 2022-04-29 DOI:10.47836/mjms.16.2.13

S. Hanif, K. A. Bhat, G. Sudhakara

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引用次数: 0

摘要

二分图G可以被视为（1,1）二分图，因为在同一部分中没有两个顶点彼此相距一个距离。（2,2）二分图是上述概念的扩展，其中同一部分中没有两个顶点彼此相距两个距离。在本文中，类似于具有最大数量的顶点对且它们之间的距离为1的完全（1，1）二分图，完全（2，2）二分图定义如下。完全（2，2）二分图是（2，2-）二分的图，并且具有最大数量的顶点对（u，v），使得d（u，v）=2。对这些图进行了刻画并研究了它们的性质。导出了几类完全（2,2）二部图的行列式、永久性和谱性质的表达式。在完全（2，2）二部图中得到了一类在其谱中具有黄金比例的图。

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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Complete (2,2) Bipartite Graphs

A bipartite graph G can be treated as a (1,1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2,2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other. In this article, analogous to complete (1,1) bipartite graphs which have the maximum number of pairs of vertices having distance one between them, a complete (2,2) bipartite graph is defined as follows. A complete (2,2) bipartite graph is a graph which is (2,2) bipartite and has the maximum number of pairs of vertices (u,v) such that d(u,v)=2. Such graphs are characterized and their properties are studied. The expressions are derived for the determinant, the permanent and spectral properties of some classes of complete (2,2) bipartite graphs. A class of graphs among complete (2,2) bipartite graphs having golden ratio in their spectrum is obtained.

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来源期刊

Malaysian Journal of Mathematical Sciences MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.