THE NON-ISOLATED DOMINATION NUMBER OF THE KRONECKER PRODUCT OF TWO GRAPHS

• Main Author: Alhanif, Rifqi
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46568
• Institution: Institut Teknologi Bandung

A subset $S$ of the vertex set $V$ of a graph $G$ is said to be non-isolated dominating set, if $S$ is a dominating set and there is no isolated vertex in the induced subgraph by $S$. The minimum cardinality taken over non-isolated dominating sets from $G$ is called the non-isolated domination number which is denoted by $\gamma_I$. Let $A$ be an $m\times n$ matrices and $B$ be a $p\times q$ matrices. If $C=A\otimes B$, then $C$ is $mp\times nq$ kronecker product matrices defined by block matrices $a_{ij}B$ for every $i\in[1,m]$ and $j\in[1,n]$. Let $A$ and $B$ be an adjacency matrices of a graph $G$ and graph $H$ respectively. The kronecker product of $G$ and $H$ is a graph whose it adjacency matrix is a kronecker product of $A$ and $B$. In this research, we provide a lower bound of the non-isolated domination number of the kronecker product of two graph. Also determine the non-isolated domination number of the kronecker product of a path and a cycle.