摘要
Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. A connected graph G is called supper-κ (resp. supper-λ) if every minimum vertex cut (edge cut) of G is the set of neighbors of some vertex in G. The g-component connectivity of a graph G, denoted by , is the minimum number of vertices whose removal from G results in a disconnected graph with at least g components or a graph with fewer than g vertices. The g-component edge connectivity can be defined similarly. In this paper, we determine the g-component (edge) connectivity of varietal hypercube for small g.
Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. A connected graph G is called supper-κ (resp. supper-λ) if every minimum vertex cut (edge cut) of G is the set of neighbors of some vertex in G. The g-component connectivity of a graph G, denoted by , is the minimum number of vertices whose removal from G results in a disconnected graph with at least g components or a graph with fewer than g vertices. The g-component edge connectivity can be defined similarly. In this paper, we determine the g-component (edge) connectivity of varietal hypercube for small g.
