Zᴋ-Magic Labeling of Path Union of Graphs

• Main Authors: P. Jeyanthi, K. Jeya Daisy, Andrea Semaničová-feňovčíková
• Format: Article
• Language: English
• Published: Universidad de La Frontera 2019-08-01
• Series: Cubo
• Subjects: a-magic labeling; zk-magic labeling; zk -magic graph; generalized petersen graph; shell; wheel; closed helm; double wheel; flower; cylinder; total graph of a path; lotus inside a circle; n-pan graph
• Online Access: http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154/1887

For any non-trivial Abelian group $A$ under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \to A-\{0\}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = \sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-\textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$, the group of integers modulo $k$ and these graphs are referred as $k$-\textit{magic} graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and $n$-pan graph are $Z_k$-magic graphs.