P. Jeyanthi; K. Jeyadaisy
Abstract
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \rightarrow A-\{0\}$ 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} ...
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For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \rightarrow A-\{0\}$ 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 $k$. These $Z_k$-magic graphs are referred to as $k$-\textit{magic} graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, $G\odot\overline{K_m}$, $m$-splitting graph of a path and $m$-shadow graph of a path are $Z_k$-magic graphs.
