Problem 3. Let (u, v) be a minimum-weight edge in a connected graph G. Show that (u, v) belongs to some minimum spanning tree of G.

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

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

Q: d e

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A: Solution:

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A:

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Q: Problem 3: Consider the following weighted graph: 5 1. Find the length of the shortest path between…

A: We need to find the shortest lenght path between a and z.We can apply the dijkstra's technique.

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A: According to the information given:-We have to define MST of an undirected graph is equivalent to a…

Q: minimum

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A: Here is the answer with explanation:-

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A: As per bartleby guidlines we answer only first three subparts .For more answers please post them…

Q: Show that a graph is 4-vertex-colourable if and only if it is the union of two bipartite subgraphs.

A: The answer of this question is as follows:

Q: Lteshe e g gl l wige bespe leof we Wf de ndid concod gh Le

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.