Monophonic Eccentric Domination Numbers of Graphs

Authors

  • Anabel E. Gamorez Western Mindanao State University
  • Sergio R. Canoy Jr. Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i2.4354

Keywords:

monophonic, eccentric, domination, join, corona, lexicographic product

Abstract

Let G be a (simple) undirected graph with vertex and edge sets V (G) and E(G), respectively.  A set S ⊆ V (G) is a monophonic eccentric dominating set if every vertex in V (G) \ S has a monophonic eccentric vertex in S. The minimum size of a monophonic eccentric dominating set in G is called the monophonic eccentric domination number of G. It is shown that the absolute difference of the domination number and monophonic eccentric domination number of a graph can be made arbitrarily large. We characterize the monophonic eccentric dominating sets in graphs resulting from the join, corona, and lexicographic product of two graphs and determine bounds on their monophonic eccentric domination numbers.

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How to Cite

Gamorez, A. ., & Canoy Jr., S. (2022). Monophonic Eccentric Domination Numbers of Graphs. European Journal of Pure and Applied Mathematics, 15(2), 635–645. https://doi.org/10.29020/nybg.ejpam.v15i2.4354

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