L(3,2,1)-labeling problem of square of path

There are many problems in graph theory, where labeling of graphs is the only alternative to solve it. Graph labeling widely appeared in frequency assignment, communication network addressing, circuit design, X-ray crystallography, coding theory, missile guidance, signal processing, etc. For any graph G = (V, E), where V is the node set and d(p, q) is the distance between nodes p and q, the L(3, 2, 1)-labeling of G is a mapping R : V -> {0, 1, 2, ...} such that |R(p) -R(q)| >= 3 if d(p, q) = 1,|R(p) -R(q)| >= 2 if d(p, q) = 2 and |R(p) -R(q)| >= 1 if d(p, q) = 3. This paper is devoted to L(3, 2, 1)-labeling of squares of path (SOP) (P-n(2)) and we obtained unique results. This is the first result about L(3, 2,1)-labeling of SOP. To the best of our knowledge, no result is available related to L(3, 2, 1)-labeling of square of any classes of graphs.