<abstract xmlns="http://www.w3.org/1999/xhtml">

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

Let 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).

Co-unit graphs associated to ring of integers modulo <italic>n</italic>

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Co-unit graphs associated to ring of integers modulo 

{"article-title":{"italic":"n","content":"Co-unit graphs associated to ring of integers modulo"}}

Let 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...

Co-unit graphs associated to ring of integers modulo n

Published Online: Jan 19, 2023

Page range: 308 - 316

Received: Dec 14, 2021

DOI: https://doi.org/10.2478/ausm-2022-0020

Keywords
unit graph, co-unit graph, ring of integers modulo n, domination number

© 2022 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Co-unit graphs associated to ring of integers modulo n

Published Online: Jan 19, 2023

Page range: 308 - 316

Received: Dec 14, 2021

DOI: https://doi.org/10.2478/ausm-2022-0020

Keywordsunit graph, co-unit graph, ring of integers modulo n, domination number

© 2022 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
unit graph, co-unit graph, ring of integers modulo n, domination number