Affiliations: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
Correspondence:
[*]
Corresponding author. Sankar Sahoo, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India. E-mail: rsmo_ssahoo@mail.vidyasagar.ac.in.
Abstract: 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
(Pn2)
, square of complete graphs
(Kn2)
and square of complete bipartite graphs
(Kp,q2)
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.
Keywords: Frequency assignment, L (3, 1, 1)-labeling, square of paths, square of complete graphs, square of complete bipartite graphs
