Analisis Rainbow Antimagic Coloring Pada Hasil Operasi Comb Graf Lintasan

Abstract

All the graphs in this paper are connected graphs. Let $G=(V,E)$ where $V(G)$ is a set of vertex from graph $G$ while $E(G)$ is a set of edge from graph $G$. A bijection function $f: V \rightarrow \{1,2,3,...,\lvert V(G)\rvert\}$ the associated weight of an edge $uv \in E(G)$ under $f$ is $W_f{(uv)}=f(u)+f(v)$. A path $P$ in a vertex-labeled graph $G$ is said to be a rainbow path if for every two edges $uv$, $u'v' \in E(P)$, there is $w_f{(uv)}\neq w_f{u'v'}$. If for every two vertices $u$ and $v$ of $G$, there is a rainbow $u$-$v$ path, then $f$ is called a rainbow antimagic labeling of $G$. A graph $G$ is rainbow antimagic if $G$ has a rainbow antimagic labeling. The minimum number of color needed to make $G$ rainbow connected, called rainbow antimagic connection number, denoted by rac(G). In this paper, we will analyze the rainbow antimagic coloring on comb product of path graph.