We define a new graph operator called the P3 intersection graph,
P3(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 P3 (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 X(G) = a, X(P3( G)) = b, where X is the chromatic number
of G. For the domination number -y(G), we construct graphs G such
that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1
and b. Similar construction for the independence number and radius,
diameter relations are also discussed.