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On Total Edge Irregularity Strength of Generalized Web Graphs and Related Graphs

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Abstract

Let G = (V, E) be a simple, connected and undirected graph with non empty vertex set V and edge set E. An edge irregular total k-labeling \({f: V(G)\cup E(G) \to \{ 1,2, \ldots, k \}}\) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights f(x) + f(xy) + f(y) and f(x′) + f(x′y′) + f(y′) are distinct. A total edge irregularity strength of graph G, denoted by 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 generalized web graph W(n, m) and two families of related graphs.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Sciences, University of Sebelas Maret, Surakarta, Indonesia

    Diari Indriati

  2. Department of Mathematics, Faculty of Mathematics and Sciences, University of Gadjah Mada, Yogyakarta, Indonesia

    Diari Indriati,  Widodo & Indah E. Wijayanti

  3. Department of Mathematics, Faculty of Mathematics and Sciences, University of Indonesia, Depok, Indonesia

    Kiki A. Sugeng

  4. Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic

    Martin Bača

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  1. Diari Indriati
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  2. Widodo
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  3. Indah E. Wijayanti
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  4. Kiki A. Sugeng
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  5. Martin Bača
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Correspondence to Martin Bača.

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Indriati, D., Widodo, Wijayanti, I.E. et al. On Total Edge Irregularity Strength of Generalized Web Graphs and Related Graphs. Math.Comput.Sci. 9, 161–167 (2015). https://doi.org/10.1007/s11786-015-0221-5

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  • DOI: https://doi.org/10.1007/s11786-015-0221-5

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