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A characterization and an application of weight-regular partitions of graphs

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A characterization and an application of weight-regular partitions of graphs. / Abiad Monge, Aida.

In: Linear Algebra and Its Applications, Vol. 569, 15.05.2019, p. 162-174.

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@article{eaec1ff554974757bf334b113c0de544,
title = "A characterization and an application of weight-regular partitions of graphs",
abstract = "A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex u is an element of V a weight that equals the corresponding entry nu(u) of the Perron eigenvector nu. This paper contains three main results related to weight-regular partitions of a graph. The first is a characterization of weight-regular partitions in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we also provide a new characterization of weight-regularity by using a Hoffman-like polynomial. As a corollary, we obtain Hoffman's result for regular graphs. In addition, we show an application of weight-regular partitions to study graphs that attain equality in the classical Hoffman's lower bound for the chromatic number of a graph, and we show that weight-regularity provides a condition under which Hoffman's bound can be improved. (C) 2019 Elsevier Inc. All rights reserved.",
keywords = "Weight-regular partition, Hoffman polynomial, Chromatic number, ALGEBRAIC CHARACTERIZATIONS",
author = "{Abiad Monge}, Aida",
note = "data source:",
year = "2019",
month = "5",
day = "15",
doi = "10.1016/j.laa.2019.01.011",
language = "English",
volume = "569",
pages = "162--174",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Science",

}

RIS

TY - JOUR

T1 - A characterization and an application of weight-regular partitions of graphs

AU - Abiad Monge, Aida

N1 - data source:

PY - 2019/5/15

Y1 - 2019/5/15

N2 - A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex u is an element of V a weight that equals the corresponding entry nu(u) of the Perron eigenvector nu. This paper contains three main results related to weight-regular partitions of a graph. The first is a characterization of weight-regular partitions in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we also provide a new characterization of weight-regularity by using a Hoffman-like polynomial. As a corollary, we obtain Hoffman's result for regular graphs. In addition, we show an application of weight-regular partitions to study graphs that attain equality in the classical Hoffman's lower bound for the chromatic number of a graph, and we show that weight-regularity provides a condition under which Hoffman's bound can be improved. (C) 2019 Elsevier Inc. All rights reserved.

AB - A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex u is an element of V a weight that equals the corresponding entry nu(u) of the Perron eigenvector nu. This paper contains three main results related to weight-regular partitions of a graph. The first is a characterization of weight-regular partitions in terms of double stochastic matrices. Inspired by a characterization of regular graphs by Hoffman, we also provide a new characterization of weight-regularity by using a Hoffman-like polynomial. As a corollary, we obtain Hoffman's result for regular graphs. In addition, we show an application of weight-regular partitions to study graphs that attain equality in the classical Hoffman's lower bound for the chromatic number of a graph, and we show that weight-regularity provides a condition under which Hoffman's bound can be improved. (C) 2019 Elsevier Inc. All rights reserved.

KW - Weight-regular partition

KW - Hoffman polynomial

KW - Chromatic number

KW - ALGEBRAIC CHARACTERIZATIONS

U2 - 10.1016/j.laa.2019.01.011

DO - 10.1016/j.laa.2019.01.011

M3 - Article

VL - 569

SP - 162

EP - 174

JO - Linear Algebra and Its Applications

T2 - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -