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Riniatul Nur Wahidah
Universitas Jember
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Pewarnaan Pelangi Antiajaib pada Amalgamasi Graf Riniatul Nur Wahidah; Dafik Dafik; Ermita Rizki Albirri
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (496.647 KB) | DOI: 10.25037/cgantjma.v3i1.76

Abstract

Let $G$ is a connected graph with vertex set $V(G)$ and edge set $E(G)$. The side weights for $uv\in E(G) $ bijective function $f:V(G)\rightarrow\{1,2,\dots, |V(G)|\}$ and $ w(uv)= f(u)+f(v) $ . If each edge has a different weight, the function $f$ is called an antimagic edge point labeling.  Is said to be a rainbow path, if a path $P$ on the graph labeled vertex $G$ with every two edges $ ,u'v'\in E(P) $ fulfill  $ w(uv)\neq w(u'v') $. If for every two vertices $u,v \in V(G)$, their path $uv$ rainbow, $f$ is called the rainbow antimagic labeling of the graph $G$. Graph G is an antimagic coloring of the rainbow if we for each edge $uv$ weight color side  $w(uv)$. The smallest number of colors induced from all sides is the rainbow antimagic connection number $G$, denoted by $rac(G)$. This study shows the results of the rainbow antimagic connection number from amalgamation graph.
Co-Authors D. Dafik Ermita Rizki Albirri