4. Let G = (V, E) be a graph with n vertices and m edges with no loops. How many l's does the incidence matrix have in it? Justify your answer.

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Please answer number 4

**4.** Let \( G = (V, E) \) be a graph with \( n \) vertices and \( m \) edges with no loops. How many 1's does the incidence matrix have in it? Justify your answer.

**5.** Draw a connected bipartite graph \( G = (V, E) \) such that its bipartition \( V_1, V_2 \) has \( |V_1| = 5 \) and \( |V_2| = 4 \) and \( \text{deg}(a) \leq 3 \) for all \( a \in V \).

- (a) Determine how many cut vertices and how many cut edges \( G \) has.
Transcribed Image Text:**4.** Let \( G = (V, E) \) be a graph with \( n \) vertices and \( m \) edges with no loops. How many 1's does the incidence matrix have in it? Justify your answer. **5.** Draw a connected bipartite graph \( G = (V, E) \) such that its bipartition \( V_1, V_2 \) has \( |V_1| = 5 \) and \( |V_2| = 4 \) and \( \text{deg}(a) \leq 3 \) for all \( a \in V \). - (a) Determine how many cut vertices and how many cut edges \( G \) has.
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