ABSTRACT
To investigate these questions, we begin with k= 3. With the following theorem, we can easily combine two 3∗-connected graphs to get another 3∗-connected graph.
THEOREM 15.1 [7]Assume that both G1 and G2 are cubic graphs, x is a vertex in G1, and y is a vertex in G2. Then J(G1,N(x);G2,N( y)) is 3∗-connected if and only if both G1 and G2 are 3∗-connected.
