L(2; 1; 1)-labeling of interval graphs

L(r; s; t)-labeling problem (Lrst-LP) is an important topic in discrete mathematics due to its various applications, like in frequency assignment in mobile communication systems, signal processing, circuit design, etc. L211 -LP is a special case of Lrst-LP. An L211-labeling (L211L) of a graph G = (V ; E) is a mapping F : V-> {0; 1; 2; ...} such that IF(xi) -F(eta)I >= 2 if and only if d(xi; eta) = 1, IF(xi) -z(eta)I > 1 if d(xi; eta) = 2 or 3, where d(xi; eta) is the distance between the nodes xi and eta. In this work, we have determined the upper bound of L211L for interval graph (IG) and obtained a tighter upper bound which is 4.6, -2. Also, we proposed an efficient algorithm to label any IG by L211L and also computed the time complexity of the proposed algorithm.