Analisa Himpunan Dominasi pada Graf-Graf Khusus

Abstract

The advance of science and technology increases proportionally to the development of era. Today era tends to the raise to the advance of ICT. One research interest which supports the ICT development is a graph theory. A dominating set theory is one of a graph theory which has a wide range of applications mainly in communication network and space syntax theory. 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 $\gamma_{k}{G}$; $k\in{\{1,2\}}$, is the order of a smallest dominating set of $G$. This research aims to find the domination number of some families of special graphs, disc brake graph $Db_{n,m}$, lampion graph $\pounds_{n,m}$, prism graph $D_{n,m}$, and staked ladder graph $Dt_{n,m}$.