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A REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF A FINITE RING
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 Title & Authors
A REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF A FINITE RING
Naghipour, Ali Reza; Rezagholibeigi, Meysam;
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 Abstract
Let R be a finite commutative ring with nonzero identity. We define to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R. This graph provides a refinement of the unit and unitary Cayley graphs. In this paper, basic properties of are obtained and the vertex connectivity and the edge connectivity of are given. Finally, by a constructive way, we determine when the graph is Hamiltonian. As a consequence, we show that has a perfect matching if and only if is an even number.
 Keywords
Cayley graphs;Clique number;Hamiltonian graphs;finite rings;matchings;unit graphs;
 Language
English
 Cited by
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