On connectivity of the semi-splitting block graph of a graph

A graph G is said to be a semi-splitting block graph if there exists a graph H such that S_B(H) ≌ G. This paper establishes a characterisation of semi-splitting block graphs based on the partition of the vertex set of G. The vertex (edge) connectivity and p-connectedness (p-edge connectedness) of S_B(G) are examined. For all integers a, b with 1 < a < b, the existence of the graph G for which κ (G) = a, κ (S_B(G)) = b and λ (G) = a, λ (S_B(G)) = b are proved independently. The characterization of graphs with κ(S_B(G)) = κ (G) and a necessary condition for graphs with κ (S_B(G)) = λ (S_B(G)) are achieved.