%0 Journal Article
%T $Z_k$-Magic Labeling of Some Families of Graphs
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Jeyanthi, P.
%A Jeyadaisy, K.
%D 2018
%\ 12/30/2018
%V 50
%N issue 2
%P 1-12
%! $Z_k$-Magic Labeling of Some Families of Graphs
%K A-magic labeling
%K $Z_k$-magic labeling
%K $Z_k$-magic graph
%K total graph
%K flower graph
%K generalized prism graph
%K closed helm graph
%K lotus inside a circle graph
%K $Godotoverline{K_m}$
%K $m$-splitting graph
%K $m$-shadow graph
%R 10.22059/jac.2018.69046
%X 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.
%U https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf