A restricted l(2,1)-labelling problem on interval graphs

In a graph G = (V, E), L(2, 1)-labelling is considered by a function pound whose domain is V and codomain is set of non-negative integers with a condition that the vertices which are adjacent assign labels whose difference is at least two and the ver-tices whose distance is two, assign distinct labels. The difference between maximum and minimum labels among all possible labels is denoted by lambda 2,1(G). This paper contains a variant of L(2, 1)-labelling problem. In L(2, 1)-labelling problem, all the vertices are L(2, 1)-lab eled by least number of labels. In this paper, maximum allowable label K is given. The problem is: L(2, 1)-label the vertices of G by using the labels {0, 1, 2, ... , K} such that maximum number of vertices get label. If K labels are adequate for labelling all the vertices of the graph then all vertices get label, otherwise some vertices remains unlabeled. An algorithm is designed to solve this problem. The algorithm is also illus-trated by examples. Also, an algorithm is designed to test whether an interval graph is no hole label or not for the purpose of L(2, 1)-labelling.