@article {
author = {Jeyanthi, P. and Jeyadaisy, K.},
title = {$Z_k$-Magic Labeling of Some Families of Graphs},
journal = {Journal of Algorithms and Computation},
volume = {50},
number = {issue 2},
pages = {1-12},
year = {2018},
publisher = {University of Tehran},
issn = {2476-2776},
eissn = {2476-2784},
doi = {10.22059/jac.2018.69046},
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} 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.},
keywords = {A-magic labeling,$Z_k$-magic labeling,$Z_k$-magic graph,total graph,flower graph,generalized prism graph,closed helm graph,lotus inside a circle graph,$Godotoverline{K_m}$,$m$-splitting graph,$m$-shadow graph},
url = {https://jac.ut.ac.ir/article_69046.html},
eprint = {https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf}
}