Efficient zero ring labeling of graphs

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

European Journal of Pure and Applied Mathematics

Volume

13

Issue

3

First Page

674

Last Page

696

Publication Date

7-2020

Abstract

A zero ring is a ring in which the product of any two elements is zero, which is the additive identity. A zero ring labeling of a graph is an assignment of distinct elements of a zero ring to the vertices of the graph such that the sum of the labels of any two adjacent vertices is not the zero element in the ring. Given a zero ring labeling of a graph, if the cardinality of the set of distinct sums obtained from all adjacent vertices is equal to the maximum degree of the graph, then the zero ring labeling is efficient. In this paper, we showed the existence of an efficient zero ring labeling for some classes of trees and their disjoint union. In particular, we showed that an efficient zero ring labeling exists for some families of the following classes of trees: path graphs, star graphs, bistars, centipede graphs, caterpillars, spiders, lobsters, and rooted trees. We also showed results for other common classes of graphs.

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Digitial Object Identifier (DOI)

https://doi.org/10.29020/nybg.ejpam.v13i3.3780

Disciplines

Mathematics

Keywords

Graph labelings; Rings (Algebra)

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