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On the k-restricted edge-connectivity of matched sum graphs

A matched sum graph G1MG2 of two graphs G1 and G2 of the same order n is obtained by adding to the union (or sum) of G1 and G2 a set M of n independent edges which join vertices in V (G1) to vertices in V (G2). When G1 and G2 are isomorphic, G1MG2 is just a permutation graph. In this work we derive bounds for the k-restricted edge connectivity λ(k) of matched sum graphs G1MG2 for 2 ≤ k ≤ 5, and present some sufficient conditions for the optimality of λ(k)(G1MG2).