A linear time algorithm to compute square of interval graphs and their colouring

Abstract The square of a graph G = ( V , E ) , denoted by G 2 , is a graph on the same vertex set V ( G ) such that two vertices x and y are adjacent in G 2 if and only if there is a path of length one or two between x and y in G . In this article, a new linear time algorithm is presented to compute G 2 from G when G is an interval graph. Also a linear time algorithm is designed to find all the maximal cliques of G 2 from G . Application of square of interval graphs in the field of L ( h , k ) -labelling problem is also discussed. Finally, it is shown that L ( 1 , 1 ) -labelling number of an interval graph can be computed in linear time.

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