Squares of Intersection Graphs and Induced Matchings

We consider the squares of intersection graphs of hypergraphs and simple graphs. The Berge-type characterization for squares of intersection graphs of hypergraphs is obtained. The analogue of Whitney theorem for squares of intersection graphs of trees is proved. Using the connection between induced matchings of graph and independent sets of square of line graph, new polynomial solvable cases for the weighted induced matching problem are obtained.