L (3, 1, 1)-labeling numbers of square of paths, complete graphs and complete bipartite graphs

• Published in: Journal of intelligent & fuzzy systems Vol. 36; no. 2; pp. 1917 - 1925
• Main Authors: Amanathulla, Sk, Sahoo, Sankar, Pal, Madhumangal
• Format: Journal Article
• Language: English
• Published: Amsterdam IOS Press BV 01.01.2019
• Subjects: Apexes; Graph theory; Graphs; Integers; Labeling; Labelling; Mapping
• ISSN: 1064-1246; 1875-8967
• DOI: 10.3233/JIFS-172195

For a graph G = (V, E) the L (3, 1, 1)-labeling is a mapping μ from the vertex set V to the set of non-negative integers {0, 1, 2, …} such that |μ (x) - μ (y) |≥3 if d (x, y) =3 and |μ (x) - μ (y) |≥1 if d (x, y) =2 or 3, where d (x, y) is the distance between the vertices x and y. λ3,1,1 (G) represents the L (3, 1, 1)-labeling number of the graph G and it is the largest non-negative integer used to label the graph G. In the present article we have studied L (3, 1, 1)-labeling of squares of some simple graphs, namely square of paths ( P n 2 ) , square of complete graphs ( K n 2 ) and square of complete bipartite graphs ( K p , q 2 ) and we obtained good results for these graph classes. The results produced in this article are unique and exact. This is the first result about L (3, 1, 1)-labeling for these graph classes.