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Co-unit graphs associated to ring of integers modulo n

Co-unit graphs associated to ring of integers modulo n AbstractLet R be a finite commutative ring. We define a co-unit graph, associated to a ring R, denoted by Gnu(R) with vertex set V(Gnu(R)) = U(R), where U(R) is the set of units of R, and two distinct vertices x, y of U(R) being adjacent if and only if x + y ∉ / U(R). In this paper, we investigate some basic properties of Gnu(R), where R is the ring of integers modulo n, for different values of n. We find the domination number, clique number and the girth of Gnu(R). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Universitatis Sapientiae, Mathematica de Gruyter

Co-unit graphs associated to ring of integers modulo n

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References (8)

Publisher
de Gruyter
Copyright
© 2022 S. Pirzada et al., published by Sciendo
eISSN
2066-7752
DOI
10.2478/ausm-2022-0020
Publisher site
See Article on Publisher Site

Abstract

AbstractLet R be a finite commutative ring. We define a co-unit graph, associated to a ring R, denoted by Gnu(R) with vertex set V(Gnu(R)) = U(R), where U(R) is the set of units of R, and two distinct vertices x, y of U(R) being adjacent if and only if x + y ∉ / U(R). In this paper, we investigate some basic properties of Gnu(R), where R is the ring of integers modulo n, for different values of n. We find the domination number, clique number and the girth of Gnu(R).

Journal

Acta Universitatis Sapientiae, Mathematica – de Gruyter

Published: Dec 1, 2022

Keywords: unit graph; co-unit graph; ring of integers modulo n; domination number; 05C50; 05C12; 05A18

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