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Herninda Lucky Oktaviana
Universitas Jember
Computer Science & IT Other

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Kajian Rainbow 2-Connected Pada Graf Eksponensial dan Beberapa Operasi Graf Herninda Lucky Oktaviana; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1460.907 KB) | DOI: 10.25037/cgantjma.v2i2.56

Abstract

Let $G=(V(G),E(G))$ is a graph connected non-trivial. \textit{Rainbow connection} is edge coloring on the graph defined as $f:E(G)\rightarrow \{1,2,...,r|r \in N\}$, for every two distinct vertices in $G$ have at least one \textit{rainbow path}. The graph $G$ says \textit{rainbow connected} if every two vertices are different in $G$ associated with \textit{rainbow path}. A path $u-v$ in $G$ says \textit{rainbow path} if there are no two edges in the trajectory of the same color. The edge coloring sisi cause $G$ to be \textit{rainbow connected} called \textit{rainbow coloring}. Minimum coloring in a graph $G$ called \textit{rainbow connection number} which is denoted by $rc(G)$. If the graph $G$ has at least two \textit{disjoint rainbow path} connecting two distinct vertices in $G$. So graph $G$ is called \textit{rainbow 2-connected} which is denoted by $rc_2(G)$. The purpose of this research is to determine \textit{rainbow 2-connected} of some resulting graph operations. This research study \textit{rainbow 2-connected} on the graph (${C_4}^{K_n}$ and $Wd_{(3,2)}\square K_n$). 
Co-Authors D. Dafik Ika Hesti Agustin, Ika Hesti