Total labelings of toroidal polyhexes. | [Science International • 2012]

Author(s):

1. Martin Baca: Department of Applied Mathematics and Informatics, Technical University, Ko?sice, Slovakia; Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan

2. Ayesha Shabbir: Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore, Pakistan

Abstract:

A toroidal polyhex is a cubic bipartite graph embedded on the torus such that each face is a hexagon. A graph G(V,E) of order p and size q is called (a,d)-edge-antimagic total if there exists a bijection f: V(G)U E(G)→{1,2,…….,p+q} such that the edge-weights, w(uv)=ƒ(u)+ ƒ(v)+ ƒ(uv), uv ε E(G), form an arithmetic sequence with the first term a and common difference d. Such a graph is called super if the smallest possible labels appear on the vertices. In this paper we study such labelings for toroidal polyhexes and give a characterization for super (a,d)-edge-antimagicness of toroidal polyhexes.

Page(s): 239-241

DOI: DOI not available

Published: Journal: Science International, Volume: 24, Issue: 3, Year: 2012

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