Dominating Sets of the Cartesian Products of Cycles
Date
2019-04-16
Authors
Assadian, Navid
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Abstract
A dominating set for a graph G is a subset D of V(G) such that every vertex
not in D is adjacent to at least one member of D. In this project, we first briefly
survey a variety of known results on dominating sets of some families of graphs,
especially the Cartesian products of two k-cycles which are our main focus for
this project.
Then, we describe the application we developed to facilitate research on
dominating sets of the Cartesian products of k-cycles. After that, we obtain
linear-time algorithms to generate dominating sets of the Cartesian products of
two k-cycles with sizes matching the best known upper bounds. Additionally,
for two cases when k is congruent to two or three modulo five, we improve the
two known upper bounds.
Description
Keywords
Dominating Sets, The Cartesian Products, Graph Theory