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$Z_k$-Magic Labeling of Some Families of Graphs | ||
| Journal of Algorithms and Computation | ||
| مقاله 1، دوره 50، issue 2، اسفند 2018، صفحه 1-12 اصل مقاله (149.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2018.69046 | ||
| نویسندگان | ||
| P. Jeyanthi* 1؛ K. Jeyadaisy2 | ||
| 1Principal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIA | ||
| 2Department of Mathematics Holy Cross College, Nagercoil, Tamilnadu, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| 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 | ||
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