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

摘要

For a graph G = (V, E) the L(3, 1, 1)-labeling is a mapping mu from the vertex set V to the set of non-negative integers {0, 1, 2, ...} such that vertical bar mu(x) - mu(y)vertical bar >= 3 if d(x, y) = 3 and vertical bar mu(x) - mu(y)vertical bar >= 1 if d(x, y) = 2 or 3, where d(x, y) is the distance between the vertices x and y. lambda(3,1,1)(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.