Question

Set H is the set of simple graphs with 8 nodes. The following statement is about the elements of H: If
in a graph the degree of all of the vertices is at least 3, then the graph is connected.
a) Decide if the statement is true or false.
b) Give the converse of the statement about the elements of H and decide if it is true or false.
Explain.

Answer 1

Answer:

Here are your answers.

Step-by-step explanation:

(a) The statement is true.

(b) (The Handle Theorem) Suppose G is 2-connected and K is a 2-connected proper subgraph of G. Then there are subgraphs L and H (the handle) of G such that L is 2-connected, L contains K, H is a simple path, L and H share exactly the endpoints of H, and G is the union of L and H.