Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph





irregular edge-weighting, equitable irregular graphs, irregularity strength,, Mongolian tent graph, polar grid graph


An k-edge-weighting of a graph G=(V,E) is a map φ: E(G) → {1, 2, 3, ..., k} where k ≥ 1 is an integer. Denote Sφ(v) is the sum of edge-weights appearing on the edges incident at the vertex v under φ.  An k-edge-weighting of G is equitable irregular if |Sφ (u)−Sφ (v)| ≤ 1, for every pair of adjacent vertices u and v in G. Theequitable irregular strength of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G and is denoted by Se (G). In this paper, we discuss the equitable irregularity of Polar grid and Mongolian tent graphs


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How to Cite

C. . Gayathri and S. Saravanakumar, “Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph”, Proyecciones (Antofagasta, On line), vol. 43, no. 3, pp. 683-694, May 2024.