In this paper, we prove that the connectivity and the edge connectivity of the lexicographic product of two graphs G1 and G2 are equal to κ1v2 and min{λ1v 2 2 , δ2 +δ1v2}, respectively, where δi, κi, λi and vi denote the minimum degree, the connectivity, the edge-connectivity and the number of vertices of Gi, respectively. We also obtain that the edge-connectivity of the direct product of K2 an...

Let $H \leq S_n$ be an intransitive group with orbits $\Omega_1, \Omega_2, \ldots ,\Omega_k$. Then certainly $H$ is a subdirect product of the direct its projections on each orbit, $H|_{\Omega_1} \times H|_{\Omega_2} H|_{\Omega_k}$. Here we provide polynomial time algorithm for computing finest partition $P$ $H$-orbits such that = \prod_{c \in P} H|_c$ and demonstrate usefulness in some applica...