Conditional connectivity of Cayley graphs generated by transposition trees

Given a graph G and a non-negative integer h  , the RhRh-(edge)connectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. Similarly, given a non-negative integer g, the g-(edge)extraconnectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has more than g   vertices. In this paper, we determine R2R2-(edge)connectivity and 2-extra(edge)connectivity of Cayley graphs generated by transposition trees.

Research highlights
► The R1R1-connectivity of Cayley graphs generated by transposition trees is determined.
► The R2R2-connectivity of Cayley graphs generated by transposition trees is determined.