Dimensi k-Metrik Pada Graf Parasut Diperumum

Abstract

Given a simple and connected graph $G=(V(G), E(G))$ and positive integer $k$. Set $S \subseteq V(G)$ is $k$-metric generator if for every pairs of distinct vertices $u,v \in V(G)$, there exists at least $k$ vertices $w_{1}, w_{2}, \ldots, w_{k} \in S$ such that $d(u,w_{i}) \neq d(v,w_{i})$ for every $i \in \{1,2,\ldots, k\}$, with $d(u,v)$ is length of shortest path form $u$ ke $v$. The $k$-metric generator with minimum cardinality is called $k$-metric bases, and the cardinalty is $k$-metric dimension of $G$denoted by $dim_{k}(G)$. This research will discuss the $k$-metric dimension of generalized parachute graphs.