\(Z_k\)-magic labeling of path union of graphs

Author
Jeyanthi, P.

Jeya Daisy, K.

Semaničová-feňovčíková, Andrea

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https://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154
10.4067/S0719-06462019000200015
Abstract
For any non-trivial Abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = ∑f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-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 Zk-magic graphs.
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