Zᴋ-Magic Labeling of Path Union of Graphs
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} gra...
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doaj-cc4f488277dc49499b61961b5917db682020-11-25T03:28:52ZengUniversidad de La FronteraCubo0716-77760719-06462019-08-01212154010.4067/S0719-06462019000200015Zᴋ-Magic Labeling of Path Union of GraphsP. Jeyanthi0K. Jeya Daisy1Andrea Semaničová-feňovčíková2Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India.Department of Mathematics, Holy Cross College, Nagercoil, Tamilnadu, India.Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic.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.http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154/1887a-magic labelingzk-magic labelingzk -magic graphgeneralized petersen graphshellwheelclosed helmdouble wheelflowercylindertotal graph of a pathlotus inside a circlen-pan graph |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
P. Jeyanthi K. Jeya Daisy Andrea Semaničová-feňovčíková |
spellingShingle |
P. Jeyanthi K. Jeya Daisy Andrea Semaničová-feňovčíková Zᴋ-Magic Labeling of Path Union of Graphs Cubo a-magic labeling zk-magic labeling zk -magic graph generalized petersen graph shell wheel closed helm double wheel flower cylinder total graph of a path lotus inside a circle n-pan graph |
author_facet |
P. Jeyanthi K. Jeya Daisy Andrea Semaničová-feňovčíková |
author_sort |
P. Jeyanthi |
title |
Zᴋ-Magic Labeling of Path Union of Graphs |
title_short |
Zᴋ-Magic Labeling of Path Union of Graphs |
title_full |
Zᴋ-Magic Labeling of Path Union of Graphs |
title_fullStr |
Zᴋ-Magic Labeling of Path Union of Graphs |
title_full_unstemmed |
Zᴋ-Magic Labeling of Path Union of Graphs |
title_sort |
zᴋ-magic labeling of path union of graphs |
publisher |
Universidad de La Frontera |
series |
Cubo |
issn |
0716-7776 0719-0646 |
publishDate |
2019-08-01 |
description |
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. |
topic |
a-magic labeling zk-magic labeling zk -magic graph generalized petersen graph shell wheel closed helm double wheel flower cylinder total graph of a path lotus inside a circle n-pan graph |
url |
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154/1887 |
work_keys_str_mv |
AT pjeyanthi zᴋmagiclabelingofpathunionofgraphs AT kjeyadaisy zᴋmagiclabelingofpathunionofgraphs AT andreasemanicovafenovcikova zᴋmagiclabelingofpathunionofgraphs |
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1724582283762991104 |