Edge-connectivity and super edge-connectivity of P2-path graphs

For a graph G, the P-2-path graph, P-2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, lambda(P-2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is super-lambda if each minimum edge cut is trivial, and it is optimum super-lambda if each minimum nontrivial edge cut consists of all the edges adjacent to one edge. We give conditions on G, for P-2(G) to be super-lambda and optimum super-lambda. (C) 2003 Elsevier B.V. All rights reserved.