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Total edge irregularity strength of accordion graphs

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Abstract

An edge irregular total k-labeling \(\varphi : V\cup E \rightarrow \{ 1,2, \dots , k \}\) 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 \(\varphi (x)+ \varphi (xy) + \varphi (y)\) and \(\varphi (x')+ \varphi (x'y') + \varphi (y')\) 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. We have determined the exact value of the total edge irregularity strength of accordion graphs.

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Acknowledgments

The authors are very grateful to the referees for their careful reading with corrections and useful comments, which improved this work very much.

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Authors and Affiliations

  1. Department of Mathematics, Comsats Institute of Information Technology, Sahiwal, Pakistan

    Muhammad Kamran Siddiqui

  2. Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

    Deeba Afzal & Muhammad Ramzan Faisal

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  1. Muhammad Kamran Siddiqui
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  2. Deeba Afzal
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  3. Muhammad Ramzan Faisal
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Correspondence to Muhammad Kamran Siddiqui.

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Siddiqui, M.K., Afzal, D. & Faisal, M.R. Total edge irregularity strength of accordion graphs. J Comb Optim 34, 534–544 (2017). https://doi.org/10.1007/s10878-016-0090-0

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  • DOI: https://doi.org/10.1007/s10878-016-0090-0

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