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On Edge Irregular Total Labeling of Categorical Product of Two Cycles

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Abstract

An edge irregular total k-labeling φ:V(G)∪E(G)→{1,2,…,k} of a graph G=(V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights φ(x)+φ(xy)+φ(y) and φ(x′)+φ(x′y′)+φ(y′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling.

In this paper, we determine the exact value of the total edge irregularity strength of the categorical product of two cycles C n and C m , for n,m≥3.

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Acknowledgements

The research for this article was supported by Slovak VEGA Grant 1/0130/12 and Higher Education Commission Pakistan Grant HEC(FD)/2007/555.

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Authors and Affiliations

  1. College of Computer Science & Information Systems, Jazan University, Jazan, Saudi Arabia

    Ali Ahmad

  2. Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovak Republic

    Martin Bača

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

    Martin Bača & Muhammad Kamran Siddiqui

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  1. Ali Ahmad
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  2. Martin Bača
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  3. Muhammad Kamran Siddiqui
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Correspondence to Martin Bača.

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Ahmad, A., Bača, M. & Siddiqui, M.K. On Edge Irregular Total Labeling of Categorical Product of Two Cycles. Theory Comput Syst 54, 1–12 (2014). https://doi.org/10.1007/s00224-013-9470-3

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  • DOI: https://doi.org/10.1007/s00224-013-9470-3

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