A Note on Edge Irregularity Strength of Some Graphs

I Nengah Suparta, I Gusti Putu Suharta


Let G(V, E) be a finite simple graph and k be some positive integer. A vertex k-labeling of graph G(V,E), Φ : V → {1,2,..., k}, is called edge irregular k-labeling if the edge weights of any two different edges in G are distinct, where the edge weight of e = xy ∈ E(G), wΦ(e), is defined as wΦ(e) = Φ(x) + Φ(y). The edge irregularity strength for graph G is the minimum value of k such that Φ is irregular edge k-labeling for G. In this note we derive the edge irregularity strength of chain graphs mK3−path for m ≢ 3 (mod4) and C[Cn(m)] for all positive integers n ≡ 0 (mod 4) 3n and m. We also propose bounds for the edge irregularity strength of join graph Pm + Ǩn for all integers m, n ≥ 3.


k-labeling; irregular edge k-labeling; irregularity strength for graph

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DOI: http://dx.doi.org/10.19184/ijc.2020.4.1.2


A.A.G. Ngurah, E. Baskoro, and R. Simanjuntak, On The Super Edge-Magic Deficiencies of Graphs, Australas. J. of Combinatorics, 40 (2008), pp. 3-14.

A. Ahmad, A. Gupta, and R. Simanjuntak, Computing the edge irregularity strengths of chain graphs and the join of two graphs, Elect. J. Graph Theory and Applications 6(1) (2018), pp. 201-207

A. Ahmad, O. Al-Mushayt, M. Bacˇa, On edge irregularity strength of graphs, Applied Mathematics and Computation 243 (2014), pp. 607-610.

I. Tarawneh, R. Hasni and A. Ahmad, On the edge irregularity strength of corona product of cycle with isolated vertices, AKCE International Journal of Graphs and Combinatorics 13 (2016), pp. 213-217.

I. Tarawneh, R. Hasni and A. Ahmad, On the edge irregularity strength of corona product of graphs with paths, Applied Mathematics E-Notes, 16 (2016), pp. 80-87.


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