A class of well-covered and vertex decomposable graphs arising from rings

Document Type : Research Paper

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.

2 Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran.

Abstract

Let Zn be the ring of integers modulo n. The unitary Cayley graph of Zn is defined as the graph G(Zn) with the vertex set Zn and two distinct vertices a,b are adjacent if and only if  a−b∈U(Zn), where U(Zn) is the set of units of Zn. Let Γ(Zn) be the complement of G(Zn). In this paper, we determine the independence number of Γ(Zn). Also it is proved that  Γ(Zn) is well-covered.  Among other things, we provide condition under which Γ(Zn) is vertex decomposable.

Keywords

References

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Algebraic Structures and Their Applications
Volume 7, Issue 2
November 2020
Pages 79-91

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