On Two Generalized Connectivities of Graphs

Abstract

The concept of generalized k-connectivity κk(G), mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. The pendant tree-connectivity τk(G) was also introduced by Hager in 1985, which is a specialization of generalized k-connectivity but a generalization of the classical connectivity. Another generalized connectivity of a graph G, named k-connectivity κ′k(G), introduced by Chartrand et al. in 1984, is a generalization of the cut-version of the classical connectivity.

Keywords

• k-connectivity
• pendant tree-connectivity
• cartesian product
• cayley graph
• 05c05
• 05c40
• 05c76