University of TehranJournal of Algorithms and Computation2476-277650issue 220181230$Z_k$-Magic Labeling of Some Families of Graphs1126904610.22059/jac.2018.69046ENP.JeyanthiPrincipal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIAK.JeyadaisyDepartment of Mathematics
Holy Cross College, Nagercoil, Tamilnadu, India.Journal Article20180630For 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.https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf