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A characterization and an application of weight-regular partitions of graphs.
- Source :
-
Linear Algebra & its Applications . May2019, Vol. 569, p162-174. 13p. - Publication Year :
- 2019
-
Abstract
- 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 ∈ V a weight that equals the corresponding entry ν u of the Perron eigenvector ν . 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 569
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134987709
- Full Text :
- https://doi.org/10.1016/j.laa.2019.01.011