1. Characterizing Irregularity in Planar Graph Structures.
- Author
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Mughal, Abdul Aleem, Jamil, Raja Noshad, and Virk, Abaid ur Rehman
- Subjects
- *
GEOMETRIC vertices , *GRAPHIC methods - Abstract
Face irregularity strength under ρ-labeling ξ with class (α1, β1, γ1) of plane graphs is a labeling from the set of graph elements into the set of integers, that is, ξ: {V ∪ E ∪ F} → {1, 2, 3, .., ρ}, such that the face weights are distinct at any stage in the graph labeling, that is, Wξ(α1,β1,γ̸1)(f) = Wξ(α1,β1,γ1)(g), for any two faces f and g of the graph G. The face irregular strength of a plane graph G is the least possible integer ρ such that G admits face irregular ρ-labeling. In this research, authors have examined the exact tight lower bounds for the face irregular strength of generalized plane graphs under ρ-labeling of class (α1, β1, γ1) for vertex (1, 0, 0), edge (0, 1, 0), face (0, 0, 1), vertex-face (1, 0, 1), edge-face (0, 1, 1) and entire (1, 1, 1). Results are verified by examples. [ABSTRACT FROM AUTHOR]
- Published
- 2023