On the Domination Number of Some Families of Special Graphs
Abstract: A domination in
graphs is part of graph theory which has many applications. Its application
includes the morphological analysis, computer network communication, social
network theory, CCTV installation, and many others. A set $D$ of vertices of a
simple graph $G$, that is a graph without loops and multiple edges, is called a
dominating set if every vertex $u\in V(G)-D$ is adjacent to some vertex $v\in
D$. The domination number of a graph
$G$, denoted by $\gamma(G)$, is the order of a smallest dominating set of $G$. A dominating set $D$
with $|D|=\gamma(G)$ is called a minimum dominating set, see Haynes and Henning
\cite{Hay1} . This research aims to find the domination number of some families
of special graphs, namely Spider Web graph $Wb_{n}$, Helmet graph $H_{n,m}$,
Parachute graph $Pc_{n}$, and any regular graph. The results shows that the
resulting domination numbers meet the lower bound of an obtained lower bound
$\gamma(G)$ of any graphs.
Author: Ika Hesti Agustin,
Dafik Dafik
Journal Code: jpmatematikagg140001