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

Abstract

[Formula: see text]-labeling problem ([Formula: see text]-[Formula: see text]) 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. [Formula: see text]-[Formula: see text] is a special case of [Formula: see text]-[Formula: see text]. An [Formula: see text]-labeling ([Formula: see text]) of a graph [Formula: see text] is a mapping [Formula: see text] such that [Formula: see text] if and only if [Formula: see text], [Formula: see text] if [Formula: see text] or 3, where [Formula: see text] is the distance between the nodes [Formula: see text] and [Formula: see text]. In this work, we have determined the upper bound of [Formula: see text] for interval graph (IG) and obtained a tighter upper bound which is [Formula: see text]. Also, we proposed an efficient algorithm to label any IG by [Formula: see text] and also computed the time complexity of the proposed algorithm.