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Total Edge Irregularity Strength of Toroidal Fullerene

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Abstract

A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. An edge irregular total k-labeling of a graph G is such a labeling of the vertices and edges with labels 1, 2, … , k that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two endvertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength, tes(G). In this paper we determine the exact value of the total edge irregularity strength of toroidal polyhexes.

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Authors and Affiliations

  1. Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovakia

    Martin Bača & Marcela Lascsáková

  2. Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

    Muhammad Kamran Siddiqui

Authors
  1. Martin Bača
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  2. Marcela Lascsáková
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  3. Muhammad Kamran Siddiqui
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Correspondence to Martin Bača.

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Bača, M., Lascsáková, M. & Siddiqui, M.K. Total Edge Irregularity Strength of Toroidal Fullerene. Math.Comput.Sci. 7, 487–492 (2013). https://doi.org/10.1007/s11786-014-0172-2

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  • DOI: https://doi.org/10.1007/s11786-014-0172-2

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