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Cycle-supermagic labelling of some classes of plane graphs

MuhammadÿNuman^a, GoharÿAli^b,*, MuhammadÿAsif^b, AndreaÿSemaničová-Feňovčíková^c

 
ABSTRACT:     A simple graph G=(V,E) admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is said to be H-magic if there exists a bijection ψ:V(G)∪E(G)→{1,2,...,|V(G)|+|E(G)|} such that for every subgraph H′ of G isomorphic to H, the sum ∑_v∈V(H′)ψ(v)+∑_e∈E(H′)ψ(e) is constant. Furthermore, G is said to be H-supermagic if ψ(V(G))={1,2,...,|V(G)|}. In this paper, we study the cycle-supermagic labelling of a pumpkin graph and two classes of planar maps containing 8-sided and 4-sided faces or 6-sided and 4-sided faces, respectively.

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* Corresponding author, E-mail: gohar.ali@icp.edu.pk

Received 8 Aug 2017, Accepted 26 Nov 2017