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Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A :
A [i][j] = 1, i <= j <= i < 5
A [i][j] = 1 indicates a directed edge from j to i
0, otherwise 
A directed spanning tree of G, rooted at r t V is defined as a sub-graph of G such that the undirected version of T is a tree and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____
    Correct answer is '24'. Can you explain this answer?
    Most Upvoted Answer
    Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices...
    When we consider a graph of two elements, we get only 1 possible MST (2-> 1) When we consider a graph of three elements, we get 2 possible MSTs (3- > 1, 3- > 2 or 2- > 1, 3- > 2) . Similarly, When we consider a graph of four elements, we get only 3 × 2×1 possible MSTs. Similarly. When we consider a graph of five elements, we get only 4 × 3 × 2 × 1 = 24 possible MSTs.
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    Community Answer
    Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices...
    Understanding the Directed Graph G
    The directed graph G is defined using the vertices V = {1, 2, 3, 4, 5} and an adjacency matrix A. The matrix indicates directed edges based on the conditions provided.
    Constructing the Directed Edges
    - The directed edges are established such that:
    - A[i][j] = 1 for i >= j (i.e., there is a directed edge from vertex j to vertex i).
    - This implies the possible directed edges are:
    - 1 ← 1
    - 2 ← 1, 2
    - 3 ← 1, 2, 3
    - 4 ← 1, 2, 3, 4
    - 5 ← 1, 2, 3, 4, 5
    Identifying Directed Spanning Trees
    - A directed spanning tree rooted at vertex 5 must include:
    - A directed path from vertex 5 to all other vertices (1, 2, 3, and 4).
    Counting the Directed Spanning Trees
    - The tree must have:
    - Vertex 5 as the root.
    - Directed edges configured such that every vertex has exactly one predecessor (except for the root).
    Combinatorial Calculations
    - The number of ways to arrange vertices 1, 2, 3, and 4 such that they can be reached from vertex 5:
    - Vertex 5 can connect to any combination of vertices 1, 2, 3, and 4.
    - Each arrangement of these vertices contributes to a unique tree.
    Final Calculation
    - The total number of directed spanning trees rooted at vertex 5 is calculated to be 24. This is derived by considering all permutations of the arrangements of the vertices, leading to a total of 4! (factorial of 4) = 24 distinct trees.
    By analyzing the directed graph and applying combinatorial principles, we conclude that the number of directed spanning trees rooted at vertex 5 is indeed 24.
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    Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A :A [i][j] = 1, i <= j <= i < 5A [i][j] = 1 indicates a directed edge from j to i0, otherwiseA directed spanning tree of G, rooted at r t V is defined as a sub-graph of G such that the undirected version of T is a tree and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____Correct answer is '24'. Can you explain this answer?
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    Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A :A [i][j] = 1, i <= j <= i < 5A [i][j] = 1 indicates a directed edge from j to i0, otherwiseA directed spanning tree of G, rooted at r t V is defined as a sub-graph of G such that the undirected version of T is a tree and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____Correct answer is '24'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A :A [i][j] = 1, i <= j <= i < 5A [i][j] = 1 indicates a directed edge from j to i0, otherwiseA directed spanning tree of G, rooted at r t V is defined as a sub-graph of G such that the undirected version of T is a tree and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____Correct answer is '24'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G (V,E) be a directed graph V = {1,2,3,4,5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A :A [i][j] = 1, i <= j <= i < 5A [i][j] = 1 indicates a directed edge from j to i0, otherwiseA directed spanning tree of G, rooted at r t V is defined as a sub-graph of G such that the undirected version of T is a tree and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is_____Correct answer is '24'. Can you explain this answer?.
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