Affiliation:
1. Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India
Abstract
Let [Formula: see text] be a commutative ring, [Formula: see text] the set of all ideals of [Formula: see text] and [Formula: see text], a subset of [Formula: see text]. The Cayley sum graph of ideals of [Formula: see text], denoted by Cay[Formula: see text], is a simple undirected graph with vertex set is the set [Formula: see text] and, for any two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] or [Formula: see text], for some [Formula: see text] in [Formula: see text]. In this paper, we study connectedness, Eulerian and Hamiltonian properties of Cay[Formula: see text]. Moreover, we characterize all commutative Artinian rings [Formula: see text] whose Cay[Formula: see text] is toroidal.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
3 articles.
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3. A Survey on Genus of Selected Graphs from Commutative Rings;Springer Proceedings in Mathematics & Statistics;2021