Generalized K-point Strong Connectivity Of Directed Graph

Generalized k-connectivity and generalized k-edge connectivity,also known as tree connec-tivity,are natural extension of connectivity and edge connectivity of undirected graph G,respec-tively.Tree connectivity has become one of the research hotspots in the field of graph theory,at-tracting the interest of many researchers.In recent years,tree connectivity of undirected graph were extended to digraph and the definition of generalized k-vertex-strong connectivity and generalized k-arc-strong connectivity were proposed by scholars.In this paper,the generalized k-vertex-strong connectivity of several digraph classes are studied.This paper is divided into the following parts:1.The research background of tree connectivity on digraphs and some preliminary knowledge used in this paper.2.Precise value for 2-vertex-strong connectivity of symmetric digraph is given.Moreover,lower sharp bound for the generalized k-arc-strong connectivity on symmetric digraph is given.3.Precise values of generalized k-vertex-strong connectivity for k ∈ {2,3,n-1,n},where D is a complete bipartite digraph of order n,are determined.4.Precise values for the generalized 2-vertex-strong and 3-vertex-strong connectivity of sev-eral Cartesian product digraph are given.5.Summary and prospect.