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COMPLETE CHARACTERIZATION OF ODD FACTORS VIA THE SIZE, SPECTRAL RADIUS OR DISTANCE SPECTRAL RADIUS OF GRAPHS

Given a graph G, a {1, 3, ..., 2n-1}-factor of G is a spanning subgraph of G, in which each degree of vertices is one of {1, 3, ..., 2n-1}, where n is a positive integer. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {1, 3...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2022, Vol.59 (4), p.1045-1067
Main Authors: Li, Shuchao, Miao, Shujing
Format: Article
Language:Korean
Online Access:Get full text
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Summary:Given a graph G, a {1, 3, ..., 2n-1}-factor of G is a spanning subgraph of G, in which each degree of vertices is one of {1, 3, ..., 2n-1}, where n is a positive integer. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {1, 3, ..., 2n-1}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {1, 3, ..., 2n-1}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.
ISSN:1015-8634