Question

here is a graph. use this graph to answer each part.
(a) how many vertices are in the graph?
(b) which of these are loops in the graph? check all that apply.
□ vp
□ ss
□ q
□ tt
□ qv
(c) which of these are edges in the graph? check all that apply.
□ vp
□ ss
□ q
□ tt
□ qv

Explanation:

Step1: Count distinct vertices

Identify each unique labeled node: S, T, U, V, R, Q, P. Count them: $7$

Step2: Identify loops (edge from vertex to itself)

Look for edges connecting a vertex to itself. Only vertex S has such an edge, so SS is the loop.

Step3: Match options to graph edges

Check each option against the graph's edges:

• VP: No edge between V and P
• SS: This is a loop (edge)
• Q: This is a vertex, not an edge
• TT: No edge from T to itself
• QV: There is an edge between Q and V

Answer:

(a) $7$
(b) SS
(c) SS, QV