Question: Does there exist a graph with five vertex incident with at least one edge l adjacent? Explain.

(a) A graph has five vertices of vertices of degree 2. How many eo

(b) A graph has degree sequence 5, 5 How many edges does it have?

Exercise: For each of the following sequences, determine if there exists a graph whose degree sequence is the one specified. In each case, either draw a graph, or explain why no graph exists.

(a) [BB] 4, 4, 4, 3, 2

(b) 100, 99, 98,...,3, 2, 2, 2

(c) [BB] 5, 5, 4, 3, 2, 1

(d) 1, l, 1, 1, 1, I

(e) 5, 4, 3, 2, 1

(f) 5,4, 3,2, 1, 1

(g) 6, 6, 4, 2, 2, 2, 1, 1