Distance Two Surjective Labelling of Paths and Interval Graphs
Sk Amanathulla, G. Muhiuddin, Deena S. Al-Kadi, Madhumangal Pal · Discrete Dynamics in Nature and Society · 2021
Graph labelling problem has been broadly studied for a long period for its applications, especially in frequency assignment in (mobile) communication system, X -ray crystallography, circuit design, etc. Nowadays, surjective L 2,1 -labelling is a well-studied problem. Motivated from the L 2,1 -labelling problem and the importance of surjective L 2,1 -labelling problem, we consider surjective L 2,1 -labelling ( SL 21 -labelling) problems for paths and interval graphs. For any graph G = V , E , an SL 21 -labelling is a mapping φ : V ⟶ 1,2 , … , n so that, for every pair of nodes u and v , if d u , v = 1 , then φ u − φ v ≥ 2 ; and if d u , v = 2 , then φ u − φ v ≥ 1 , and every label 1,2 , … , n is used exactly once, where d u , v represents the distance between the nodes u and v , and n