On efficient zero ring labeling and restricted zero ring graphs

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

European Journal of Pure and Applied Mathematics

Volume

14

Issue

1

First Page

268

Last Page

277

Publication Date

2021

Abstract

In [3], Acharya et al. introduced the notion of a zero ring labeling of a connected graph G, where vertices are labeled by the elements of a zero ring such that the sum of the labels of adjacent vertices is not the additive identity of the ring. Archarya and Pranjali [1] also constructed a graph based on a finite zero ring called the zero ring graph. In [5], Chua et al. defined a class of zero ring labeling called efficient zero ring labeling and it was shown that a labeling scheme exists for some families of trees. In this paper, we provide an efficient zero ring labeling for some classes of graphs. We also introduce the notion of the restricted zero ring graphs and use them to show that a zero ring labeling exists for some classes of cactus graphs.

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Digitial Object Identifier (DOI)

https://doi.org/10.29020/nybg.ejpam.v14i1.3890

Disciplines

Mathematics

Keywords

Graph labelings; Rings (Algebra)

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