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

For a graph G, the P2-path graph, P2(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, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum superif each minimum nontrivial edge cut consists of all the edges adjacent to one edge. We give conditions on G, for P2(G) to be superand optimum super. c © 2003 Elsevier B.V. All rights reserved.