A Cvetkovic-type Theorem for coloring of digraphs

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In 1972, Cvetkovic proved that if G is an n-vertex simple graph with the chromatic number k, then its spectral radius is at most the spectral radius of the n-vertex balanced complete k-partite graph. In this paper, we analyze the characteristic polynomial of a digraph D to prove a tight upper bound for the spectral radius of D in terms of the number of vertices and the chromatic number of D; we also characterize when equality holds. This provides a simple proof of a result by Lin and Shu [6]. (C) 2021 The Authors. Published by Elsevier Inc.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2022-02
Language
English
Article Type
Article
Citation

LINEAR ALGEBRA AND ITS APPLICATIONS, v.634, pp.30 - 36

ISSN
0024-3795
DOI
10.1016/j.laa.2021.10.022
URI
http://hdl.handle.net/10203/289649
Appears in Collection
MA-Journal Papers(저널논문)
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