@article{Koam2023, 
author = {Ali N. A. Koam and Ali Ahmad and Martin Bača and Andrea Semaničová-Feňovčíková},
title = {Modular edge irregularity strength of graphs},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1475-1487},
keywords = {(modular) irregular labeling, (modular) irregularity strength, (modular) edge irregularity strength, caterpillar, cycle, friendship graph, n-sun},
url = {https://www.sciopen.com/article/10.3934/math.2023074},
doi = {10.3934/math.2023074},
abstract = {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.}
}