Open AccessMonophonic Eccentric Domination Numbers of Graphs
Author(s) -
Anabel Enriquez Gamorez,
Sergio R. Canoy
Publication year - 2022
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v15i2.4354
Subject(s) - mathematics , vertex (graph theory) , combinatorics , lexicographical order , eccentric , graph , domination analysis , undirected graph , connectivity , physics , quantum mechanics
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.