Connectivity measures in matched sum graphs

AbstractA matched sum graph G of two graphs G1 and G2 of the same order is obtained from the union of G1 and G2 and from joining each vertex of G1 with one vertex of G2 according to one bijection f between the vertices in V(G1) and V(G2). When G1=G2=H then f is just a permutation of V(H) and the corresponding matched sum graph is a permutation graph Hf. 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