The Girth of the Total Graph of ℤ_n

DOI

10.2991/assehr.k.210508.080How to use a DOI?

Keywords

Total graph, Commutative ring, Zero divisors, Girth

Abstract

Let R be a commutative ring with a non-zero identity, and Z(R) is a set of zero-divisors of R. The total graph of R, denoted TΓ(R), is an (undirected) graph with all elements R as vertices of TΓ(R) and for distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ Z(R). The girth of TΓ(R) is the length of the shortest cycle in TΓ(R), its denoted by gr(TΓ(R)). In this paper, we discuss the characterization of the total graph of ℤn, TΓ(ℤn) and gr(TΓ(ℤn)).

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Rafika Dwi Any
AU  - Indriati Nurul Hidayah
PY  - 2021
DA  - 2021/05/11
TI  - The Girth of the Total Graph of ℤn
BT  - Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
PB  - Atlantis Press
SP  - 308
EP  - 310
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.210508.080
DO  - 10.2991/assehr.k.210508.080
ID  - Any2021
ER  -