Regular graphs with a cycle as a star complement

Zoran Stanic´

doi:10.47443/dml.2024.141

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Regular graphs with a cycle as a star complement

Author(s)

Zoran Stanic´ Faculty of Mathematics, University of Belgrade,Studentski trg 16, 11 000 Belgrade,Serbia

Abstract

Let G be an n-vertex graph having an eigenvalue of multiplicity k. A star complement for in G is an induced subgraph H with n k vertices, such that is not its eigenvalue. In the case when H is a t-vertex cycle Ct with t 3, it is shown that G is regular if and only if 2 f3; 1; 0; 1; 2g. For = 3 and = 1, G is the complete graph K4 and the Petersen graph, respectively. For 2 f0; 1g, a structural characterization of infinite families of graphs that appear in the role of G is given, and their existence is shown. The obtained results, together with the result of [F. K. Bell, Linear Algebra Appl. 296 (1999) 15-25] concerning = 2, establish a complete characterization of regular graphs having Ct as a star complement for some eigenvalue.

Publication Details

Page(s) 70-76

DOI 10.47443/dml.2024.141

Published Journal: Discrete Mathematics Letters, Volume: 14, Issue: 0, Year: 2024

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Keywords

Adjacency Matrix, circulant graph, regular graph, star complement, inverse

References

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