A characterization of weight-regular partitions of graphs

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.050

Aida Abiad

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引用次数: 0

Abstract

A partition $P = {V_{1}, \dots, V_{m}}$ of the vertex set V of a graph is regular if, for all i, j, the number of neighbors which a vertex in V_i has in the set V_j is independent of the choice of vertex in V_i. The natural generalization of a regular partition, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex $u \in V$ a weight which equals the corresponding entry $ν_{u}$ of the Perron eigenvector ν. In this work we investigate when a weight-regular partition of a graph is regular in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we provide a new characterization of weight-regular partitions by using a Hoffman-like polynomial.

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图的权规则分区的表征

分区P = {V1,…,Vm}的顶点集合V图是常规,如果我,j,邻居一个顶点在Vi的数量设置Vj是独立的顶点在Vi的选择。一个常规的自然推广分区,为非正式图也很有意义,是所谓的weight-regular分区,使每个顶点u V∈重量等于相应的条目ν阶石特征向量ν的u。在这项工作中，我们研究了当一个图的权重正则划分在双随机矩阵中是正则的。受Hoffman正则图刻画的启发，我们利用类Hoffman多项式给出了权重正则分区的一种新的刻画。

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

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.