Total reflexive edge irregularity strength of staircase graphs and related graphs
M. Basherm.basher@qu.edu.samohamed.basher@sci.suezuni.edu.egDepartment of MathematicsCollege of ScienceQassim UniversityBuraydah, 51452, Saudi Arabia0000-0003-4576-1586View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 27 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2689
- Pages:
- 1–15
Abstract
Ryan proposed the concept of reflexive edge irregular labeling of graphs in 2017. The reflexive edge irregular total m-labeling on graph Ω with vertex set VΩ and edge set EΩ is defined as a mapping ve from the edge set EΩ to the whole positive numbers {1, 2, ..., me} and a mapping vv from the vertex set VΩ to the even positive numbers {0, 2, ..., 2mv} such that v(x) = vv (x) if x ∈ VΩ and v(xy) = ve (xy) if xy ∈ EΩ, where m = max{me, 2mv}. For each xy ∈ EΩ, we have a weight wt(xy) = v(x) + v(y) + v(xy). The lowest value m utilized in reflexive total m-labeling is referred to as the reflexive irregularity strength of the graph Ω. Symbolized by res(Ω). In this research, we computed the precise value of reflexive edge irregularity strength for staircase graphs, double staircase graphs, and mirror-staircase graphs.
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References
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