The P3 intersection graph

We define a new graph operator called the P-3 intersection graph, P-3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given. Forbidden subgraph characterization for P-3(G) having properties of being chordal, H-free, complete are also obtained. For integers a and b with a > 1 and b >= a - 1, it is shown that there exists a graph G such that chi(G) = a, chi(P-3(G)) = b, where chi is the chromatic number of G. For the domination number gamma(G), we construct graphs G such that gamma(G) = a and gamma(P-3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed.