Connectivity measures in matched sum graphs

A matched sum graph G of two graphs G(1) and G(2) of the same order is obtained from the union of G(1) and G(2) and from joining each vertex of G(1) with one vertex of G(2) according to onebijection.f between the vertices in V(G(1)) and V(G(2)). When G(1) =G(2) = H then f is just a permutation of V (H) and the corresponding matched sum graph is a permutation graph H-f. In this paper, we derive lower bounds for the connectivity, edge-connectivity, and different conditional connectivities in matched sum graphs, and present sufficient conditions which guarantee maximum values for these conditional connectivities. (C) 2007 Elsevier B.V. All rights reserved.