On graph-(super)magic labelings of a path-amalgamation of isomorphic graphs
نویسندگان
چکیده
A graph G = (V (G), E(G)) admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is H-magic if there exists a bijection f : V (G)∪E(G)→ {1, 2, 3, . . . , |V (G)∪E(G)|} such that for every subgraph H ′ of G isomorphic to H, ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e) is constant. Then G is H-supermagic if f(V (G)) = {1, 2, 3, . . . , |V (G)|}. Let {Gi}i=1 be a finite collection of graphs and each Gi contains a path P i n on n vertices called a terminal path. The path amalgamation Amal{Gi, P i n, k} is formed by taking all of the Gi’s and identifying their terminal paths. Let G be a connected graph. In this paper, we study G-(super)magic labelings of Amal{Gi, P i n, k} where Gi ∼= G. We give a sufficient condition for Amal{Gi, P i n, k} to be G-(super)magic.
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