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Two types irregular labelling on dodecahedral modified generalization graph.

Nurdin Hinding1, Kiki A Sugeng2, Nurlindah3

  • 1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin, Indonesia.

Heliyon
|November 10, 2022
PubMed
Summary

This study explores irregular graph labeling on modified dodecahedral graphs. Researchers determined the total vertex irregularity strength and modular irregularity strength for these specific graph structures.

Keywords:
Dodecahedral graphIrregular labellingModular irregularity strengthTotal vertex irregularity strength

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Area of Science:

  • Graph Theory
  • Discrete Mathematics
  • Network Science

Background:

  • Irregular labeling assigns distinct weights to graph components (vertices/edges).
  • This concept is crucial for understanding graph properties and network structures.
  • Previous research has explored irregular labeling on various graph classes.

Purpose of the Study:

  • To investigate two types of irregular labeling on modified dodecahedral graphs.
  • To determine the total vertex irregularity strength for these graphs.
  • To determine the modular irregularity strength for these graphs.

Main Methods:

  • Focus on dodecahedral modified generalized graphs.
  • Application of irregular labeling principles to vertices and edges.
  • Calculation of specific irregularity strength metrics.

Main Results:

  • The total vertex irregularity strength of modified dodecahedral graphs was determined.
  • The modular irregularity strength of modified dodecahedral graphs was determined.

Conclusions:

  • The findings provide exact values for irregularity strengths in this graph class.
  • These results serve as a basis for analyzing similar graph structures.
  • The study contributes to the broader understanding of irregular graph labeling.