Title of article :
A class of well-covered and vertex decomposable graphs arising from rings
Author/Authors :
Vafaei, Morteza Department of Mathematics - Science and Research Branch Islamic Azad University (IAU), Tehran, Iran , Tehranian, Abolfazl Department of Mathematics - Science and Research Branch Islamic Azad University (IAU), Tehran, Iran , Nikandish, Reza 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 :
Independence number , Complete graph , Well-covered , Clique number , Vertex decomposable
Journal title :
Journal of Algebraic Structures and Their Applications
