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Research articles

ScienceAsia 44(2018): 129-134 |doi: 10.2306/scienceasia1513-1874.2018.44.129


Cycle-supermagic labelling of some classes of plane graphs


Muhammad Numana, Gohar Alib,*, Muhammad Asifb, Andrea Semaničová-Feňovčíkovác

 
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 ∑vV(H′)ψ(v)+∑eE(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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a Department of Mathematics Comsats Institute of Information Technology, Attock, Pakistan
b Department of Mathematics Islamia College, Peshawar, Pakistan
c Department of Applied Mathematics and Informatics, Technical University, Ko¡ice, Slovak Republic

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

Received 8 Aug 2017, Accepted 26 Nov 2017