Efficient Zero Ring Labeling of Graphs

Authors

  • Dhenmar Enriquez Chua De La Salle University http://orcid.org/0000-0002-5075-6987
  • Francis Joseph Hernandez Campeña De La Salle University
  • Floresto Franco Mariano Marcos State University

DOI:

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

Keywords:

efficient zero ring labeling, zero ring labeling, zero ring

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.

Author Biography

  • Francis Joseph Hernandez Campeña, De La Salle University
    Assistant Professor, Mathematics and Statistics Department

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Published

2020-07-31

Issue

Vol. 13 No. 3: (July 2020)

Section

Nonlinear Analysis

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How to Cite

Efficient Zero Ring Labeling of Graphs. (2020). European Journal of Pure and Applied Mathematics, 13(3), 674-696. https://doi.org/10.29020/nybg.ejpam.v13i3.3780