Unitary Cayley Graphs for Finite Rings
نویسندگان
چکیده
Given an integer n, one defines the unitary Cayley graph, denoted Cay(Zn,Zn), to be the graph whose vertex set is Zn, the integers modulo n, with an edge between two vertices x, y if x− y is a unit in (the ring) Zn. Unitary Cayley graphs have been studied as objects of independent interest (see, for example, [3], [2], [7], [8], [9]) but are of particular relevance in the study of graph representations, begun in [5] and continued in many other papers. A graph is said to be representable modulo n if it is isomorphic to an induced subgraph of Cay(Zn,Zn), and so the central problem in graph representations is to determine the smallest positive n modulo which a given graph G is representable. It is natural, then, to study unitary Cayley graphs in the hope of gaining insight into the graph representation problem.
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