Zᴋ-Magic Labeling of Path Union of Graphs
| Autor: | P. Jeyanthi, K. Jeya Daisy, Andrea Semaničová-feňovčíková |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Cubo, Vol 21, Iss 2, Pp 15-40 (2019) |
| Druh dokumentu: | article |
| ISSN: | 0719-0646 0716-7776 |
| DOI: | 10.4067/S0719-06462019000200015 |
| Popis: | For any non-trivial Abelian group $A$ under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \to A-\{0\}$ 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 $k$ and these graphs are referred as $k$-\textit{magic} graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and $n$-pan graph are $Z_k$-magic graphs. |
| Databáze: | Directory of Open Access Journals |
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