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The reflexive edge strength on some almost regular graphs.

Ika Hesti Agustin1,2, Dafik3, M Imam Utoyo2

  • 1CGANT-University of Jember, Indonesia.

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Summary
This summary is machine-generated.

This study defines edge irregular reflexive k-labeling for graphs. Researchers determined the reflexive edge strength for graphs with nearly regular vertex degrees.

Keywords:
Edge irregular reflexive k-labelingLadder graphReflexive edge strengthTriangular ladder

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Area of Science:

  • Graph Theory
  • Combinatorics
  • Discrete Mathematics

Background:

  • Introduces total k-labeling, assigning numbers to graph edges and vertices.
  • Defines edge irregular reflexive k-labeling, where adjacent edges and incident edges/vertices have distinct sums.
  • Establishes reflexive edge strength (χ'(G)) as the minimum k for such a labeling.

Purpose of the Study:

  • Determine the reflexive edge strength for specific graph classes.
  • Investigate graphs exhibiting near-regularity in vertex degrees.

Main Methods:

  • Utilized graph labeling techniques.
  • Applied combinatorial methods to analyze graph properties.
  • Focused on graphs with vertex degrees showing almost regularity.

Main Results:

  • Derived the reflexive edge strength for graphs with vertex degrees exhibiting almost regularity.
  • Provided specific values or bounds for χ'(G) in these graph classes.

Conclusions:

  • The study contributes to understanding graph labeling invariants.
  • Results offer insights into the structure of graphs with near-regular vertex degrees.