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, λ(P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is super-λ if each minimum edge cut is trivial, and it is optimum super-λ if each minimum nontrivial edge cut consists of all the edges adjacent to one edge. We give conditions on G, for P2(G) to be super-λ and optimum super-λ.

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