University of Tehran Journal of Algorithms and Computation 2476-2776 50 issue 2 2018 12 30 $Z_k$-Magic Labeling of Some Families of Graphs 1 12 69046 10.22059/jac.2018.69046 EN P. Jeyanthi Principal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIA K. Jeyadaisy Department of Mathematics Holy Cross College, Nagercoil, Tamilnadu, India. Journal Article 2018 06 30 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, $Godotoverline{K_m}$, $m$-splitting graph of a path and  $m$-shadow graph of a path are $Z_k$-magic graphs. https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf