Analisis Rainbow Vertex Connection pada Beberapa Graf Khusus dan Operasinya - Ida Ariska; Dafik Dafik; Ika Hesti Agustin (CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 2021)
Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with edge coloring defined as $c:E(G) → \{1,2,...,k\} ,k \in N$, with the condition that neighboring edges can be the same color. An original path is {\it rainbow path} if there are no two edges in the path of the same color. The graph $G$ is called rainbow connected if every two vertices in $G$ with rainbow path in $G$. The coloring here is called rainbow coloring, and the minimal coloring in a graph $G$ rainbow connection number is denoted by $rc(G)$. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with a vertex coloring defined as $c':V(G) → \{1,2,...,k\},k \in N$, with the condition that neighboring interior vertex may have the same color. An original path is rainbow vertex path if there are no two vertices in the path of the same color. The graph $G$ is called rainbow vertex connected if every two vertices in $G$ with rainbow vertex path in $G$. The $G$ coloring is called rainbow vertex coloring, and the minimal coloring in a $G$ graph is called rainbow vertex connection number which is denoted by $rvc(G)$. This research produces rainbow vertex connection number on the graph resulting from the operation amal($Bt_{m}$, $v$, $n$), $Wd_{3,m}$ $\Box$ $ P_n$, $P_m$ $\odot$ $Wd_{3,n}$, $Wd_{3,m}$ $+$ $C_n$, and shack($Bt_{m}$, $v $, $n$).