(h) Given an undirected graph G and weights w, for each vertex v, compute a vertex cover S minimizing ves Wv. VES

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A: A graph is a mathematical representation of a network consisting of nodes and edges. The nodes…

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A: Euler:- 1) A graph is Euler if and only if the degree of every vertex is even.

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A: Оne  аlgоrithm  fоr  finding  the  shоrtest  раth  frоm  а  stаrting  nоde  tо  а  tаrget  nоde  in…

Q: Connectivity in Directed and Undirected Graphs]

A: Given :-In the above mentioned question, the statements following are mentioned

Q: in theory graph 3.14 Characterize graphs G for which Y(G) +Y₂(G) = p. Igung to ylimal

A: The question has been answered in step2

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A: See below step for explanation.

Q: Prove that if a graph with n vertices and medges is planar and bipartite then m≤2n-4.

A: To prove that if a graph with n vertices and m edges is planar and bipartite, then m ≤ 2n - 4, we…

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A: According to the information given:- We have to follow the graph and find the source and sink , one…

Q: 1. Assume that G is a triangle-free planar graph with v vertices and e edges. Let K3,3 denotes the…

A: Here is the answer with explanation:-

Q: Q 6 - Show that if a graph G is Eulerian then each of its blocks is Eulerian. Is the converse true?

A: Suppose the graph is 2-connected. It implies that there is nothing to prove because the graph is the…

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A: Let us consider a graph in which there are N vertices numbered from 0 to N-1 and E number of…

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A: Pre- and Post- Order Correspondence, Suppose that for a graph G you are given the list of the…

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A: Given a directed graph G consisting of four nodes : 2,3,4,1 . The above graph is directed because it…

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A: In this question we have been given with the graph and we have to answer for the graph theory…

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A: Adjacency matrix is a way to describe the relationships between nodes in a graph.Transitive closure…

Q: 15 b 21 14 c 17 d 00 2. 1.

A: Initialize distances from the source to all vertices as infinite and distance to the source itself…

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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…

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A: The question is on finding shortest path from a node to all nodes of Graph.

Q: Let G be the following graph. Do not have to show an explanation for your answers in this problem.…

A: The graph is Eulerian graph or not is detailed in step 2.

Q: (d) Given a directed graph G, determine if there exists a collection of one or more cycles C1,...,…

A: The solution is given in step

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A: Given graph contains, 6 vertices {A, B, C, D, E, F} and 8 edges {AB, AE, AD, BC, CE, DE, EF, CF} .

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A: strongly connected components are defined as the vertex from where we reach to the each and every…

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A: We will prove the statement by induction on the number of vertices, v. Base case: If v = 3, then the…

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A: an example of a problem is the input specified in the problem.a example of a problem with the…

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A: Adjacency list of a graph is a representation of the graph where the connections between nodes is…

Q: (a) What is the smallest expansion cut in a cycle with n nodes. (b) What is the densest subgraph in…

A: below I have provided the solution of the given question

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A: The answer of this question is as follows:

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Q: 8. The number of edges of the complete graph Ks is.

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Q: Find a and b.

A: Given that  total vertices V = 18 Total edges E = 53 a vertices have degree 7  b vertices have…

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A: Number of connecting edge from a vertex is known as degree of vertex.

Q: (grapg theory) Prove that if P and Q are two longest paths in a connected graph, then P and Q have…

A: Solution:   Given,  Prove that if P and Q are two longest paths in a connected graph, then P and Q…

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A:

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A: Lets discuss the solution in the next steps

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A: Here in this question we have given a degree sequence 1,1,1,2,3,4,5,7,and we have asked weather any…