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UTK Notes


11.9.2023

Question 1: Consider the 10-vertex graph $G$ below. What type of graph property does the 6-vertex subgraph of red vertices and edges have relative to graph $G$?

Graph.jpg

(3 points)

A. spanning
B. induced
C. complete
D. none of the above

Answer B. induced

Question 2: How many distinct $K_{3}$ subgraphs are in the 10-vertex graph $G$ below?

Graph.jpg

(3 points)

A. 0
B. 1
C. 2
D. 3

Answer C. 2

Question 3: Consider the 10-vertex graph $G$ below, consider the 4-vertex subgraph $G_{1}$ defined by the vertex set $V_{1} = \{f, h, i, j\}$. Which of the following subgraphs (defined by their vertex sets) is isomorphic to $G_{1}$?

Graph.jpg

(3 points)

A. $V_{2} = \{a, b, e, f\}$
B. $V_{3} = \{a, b, g, h\}$
C. $V_{4} = \{a, b, f, j\}$
D. $V_{5} = \{a, g, h, i\}$

Answer D. $V_{5} = \{a, g, h, i\}$

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