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- W2949325087 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 $uin V$ a weight that equals the corresponding entry $nu_u$ of the Perron eigenvector $mathbf{nu}$. 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." @default.
- W2949325087 created "2019-06-27" @default.
- W2949325087 creator A5078358817 @default.
- W2949325087 date "2018-07-20" @default.
- W2949325087 modified "2023-09-26" @default.
- W2949325087 title "A characterization and an application of weight-regular partitions of graphs" @default.
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- W2949325087 doi "https://doi.org/10.48550/arxiv.1807.07809" @default.
- W2949325087 hasPublicationYear "2018" @default.
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