AIMS Mathematics (Jan 2023)

Modular edge irregularity strength of graphs

  • Ali N. A. Koam,
  • Ali Ahmad,
  • Martin Bača,
  • Andrea Semaničová-Feňovčíková

DOI
https://doi.org/10.3934/math.2023074
Journal volume & issue
Vol. 8, no. 1
pp. 1475 – 1487

Abstract

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For a simple graph G=(V,E) with the vertex set V(G) and the edge set E(G), a vertex labeling φ:V(G)→{1,2,…,k} is called a k-labeling. The weight of an edge under the vertex labeling φ is the sum of the labels of its end vertices and the modular edge-weight is the remainder of the division of this sum by |E(G)|. A vertex k-labeling is called a modular edge irregular if for every two different edges their modular edge-weights are different. The maximal integer k minimized over all modular edge irregular k-labelings is called the modular edge irregularity strength of G. In the paper we estimate the bounds on the modular edge irregularity strength and for caterpillar, cycle, friendship graph and n-sun we determine the precise values of this parameter that prove the sharpness of the lower bound.

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