Problem 4: Graphs and Relations Consider an arbitrary directed graph G = (V, E). [a] How is E related to the concept of Cartesian product? [b] Let A be a binary relation over V X V such that vAw means that vertex v is adjacent to vertex w. Discuss whether the relation A is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, or transitive. [c] Let C be a binary relation over V X V such that vCw means that that vertex v is connected to vertex w. Discuss whether the relation C is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, or transitive.

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A: - We need to talk about matrix and adjacency list representation for the graph mentioned.

Q: .(a) Assume there is an adjacency matrix A of an undirected graph G. Further assume a 1 is indicated…

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A: Adjacency matrix A:

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A: So one thing you must remember is that a spanning has always has only one incoming edge and has only…

Q: Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

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A: ANSWER:-

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A:

Q: Find a and b.

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A: The above question is solved in step 2:-

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A: According to the information given:- We have to find in correct option to satisfy the condition.

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A: Ans a)

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Q: 2. Draw the directed graph of the reflexive closure of the relations with the directed graph shown.

A: to make reflexive closure,we have to add all selfloops of the edges .

Q: (b) Draw a directed graph representation of R.

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A: Dear Student, The correct answer to both your questions along with required explanation is given…