(g) Given a weighted, connected undirected graph G and an edge e, compute the lowest-weight spanning tree of G that includes e.

Q: Q2; find all spanning tree for the following graph

A: We know that , given a graph G = V , E , a subgraph of G that connects all vertices and it is a tree…

Q: . Let G be a connected graph and e be a bridge in G. Must e be contained in any spanning tree of G?…

A: We will form any arbitrary graph G  in which  'e' will be a bridge and then show e must be contained…

Q: Give a simple example of a connected graph such that an edge (u, v) is a light edge for some cut,…

A: Considering an example of a triangle, whose all weights of edges are equal. This is an example of…

Q: 11. Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

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Q: (a) (b)

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Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Simply keep in mind that vertex degree multiplied by number of vertices is two times number of…

Q: Suppose a graph G is regular of degree r, where r is odd. (a) prove that G has an even even number…

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Q: Let G be connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning…

A: The weight of minimum spanning set

Q: Find the number of distinct spanning trees of the complete graph K4

A: * ANSWER :-    The spanning tree is a subset of graph G , which has all the vertices covered with…

Q: 12. Let G be a graph in which there is no pair of adjacent edges. What can you say about the degree…

A: See picture

Q: 3. Draw all spanning trees of the following graph shown below. b

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Q: Find all spanning trees of this graph:

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Q: 3. Find the minimal Spanning tree for the following graph. Consider "C" as the starting node. 8 B

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Q: (a) Prove that if a connected planar graph has 13 vertices and 12 edges then it must be a tree. (b)…

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Q: Select the graph that is a spanning tree for the given graph.

A: A spanning tree of a connected graph G can be defined as a maximal set of edges of graph G that…

Q: Use the pigeonhole principle to prove that a graph has at least two vertices with the same degree

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Q: Prove that if u is a vertex of odd degree in a graph, then there exists a path from u to another…

A: We have to prove :       If u is a vertex of odd degree in a graph, then there exists a path from…

Q: Find a spanning tree for the connected graph. OA. OB. Oc. OD.

A: General properties of spanning tree: A spanning tree is a subset of Graph G, which has all the…

Q: w Graph A

A: Solution A: Given graph is Using Kirchhoff's Law: For find the number of spanning tree, we have to…

Q: Let G be a graph with n vertices. Prove that if G is connected and has n 1 edges, then G is a tree.…

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Q: 3. A labeled Ks graph with labeled edges appears below. Which edge permutation is induced by the…

A: Solution:

Q: Let G be a graph on n vertices (with no loops or multiple edges). Prove that if all vertices in G…

A: 1. A graph G is an ordered pair (V(G), E(G)) consisting of a non-empty set V(G) of vertices and a…

Q: Find a subgraph H of the graph G given below that has 4 vertices and 3 edges.

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Q: Find all the spanning Trees in the following graph? Also mention those spanning trees which are…

A: Explanation : From the following diagram adjacency matrix should be find , so that the over-all…

Q: Draw a directed graph with as few edges as possible that is strongly-connected, has 8 vertices of…

A: Strongly connected directed 8 vertices one has in-degree 3 two have cut degree 3 rest have samller…

Q: For a connected graph G, prove that an edge e is in every possible spanning tree of G iff removing e…

A: Proof by contradiction

Q: Find two different spanning trees in the following graph. Clearly mark the edges and vertices that…

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Q: (a) G is a connected graph with 6 vertices and 5 articulation points.

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Q: If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify

A: In order to find the solution of the given question, we will use the concept of Hamiltonian graph…

Q: Let H be a simple graph on n vertices that has m edges. Prove that H contains at least m – n +1…

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Q: 11. > Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

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Q: 2. Suppose G is a planar graph having 67 edges. If each face of G has length at least 6, then what…

A: From the given information. The number of edges (e) = 67 The number of vertices at each face (v) = 6

Q: A minimum spanning tree is a loop.  A. True  B. False

A: Given: To determine a minimum spanning tree is a loop as follows,A. True  B. False

Q: A graph G with 7 vertices consists of two copies of K4 that share a single vertex. The vertices are…

A: The objective here is to find the number of distinct labeled spanning trees of G. Given: G is graph…

Q: 1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the…

A: 1. It is given that the graph is directed and finite.Therefore it has finite vertex and it is given…

Q: Let G be a pseudograph with 6 vertices. If G is having 3 loops and no parallel or multiple edges,…

A: A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted.…

Q: How many spanning trees are can be generated from its graph? Define 2 spanning trees of Graph A and…

A: We have to solve the given questions

Q: If a graph with six vertices is embedded in S?, what is the maximum number of edges it can have.…

A: Consider the provided question, A graph G is embedable on S2 if it is embedable on a plane. Since,…

Q: Is there an edge in a graph such that which does not appear in any spanning tree?

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Q: Let G be a connected graph with at least two nodes. Prove that it has a node such that if this node…

A: Consider a connected graph with at least two vertices. choose vertices u,v so that du,v=maximum if…

Q: Gis a connected graph with 32 vertices and 41 edges A spanning tree for G has vertices and edges

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Q: Let G be a graph with n vertices and an independent set of size s ≥ 1. What is the maximum possible…

A: Please check the next step for details

Q: B. Find all spanning trees of the following graph.

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Q: A spanning tree of a connected simple graph G is a circuit-free subgraph that contains all the…

A: The following steps are used to find the minimum spanning tree by Kruskal's algorithm. Tabulate all…

Q: 2. Draw four spanning trees of graph G. d.

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Q: Determine the minimum spanning tree T for the graph with weight G in the figure below: 3

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Q: Show that the Petersen graph is nonplanar. [Hint: show that the graph is edge contractible to Ks).

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: a. By using Kruskal's algorithm, construct the minimal spanning tree for the following graph. Also…

A: a) By using Kruskal's Algorithm:    Step:1 Remove parallel edges and loops, in the given graph there…

Q: no of edges for a tree with number of vertices 10 is

A: