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Q: In each part, either draw a graph with the given specifications or explain why no such graph exists.…

A: Here  means a complete bipartite graph with vertices partition  so that whose graph look like this :

Q: Calculate the number of paths of length 10 starting at the vertex 1. How many of these paths end at…

A: We will use the fact that if A is the adjacency matrix of a graph .Then the number of paths of…

Q: Construct a connected bipartite graph that is not a tree with vertices O, P, Q, R, S, T. What is the…

A:

Q: Quèstion 16 If a Graph has 10 vertices each of degree 5, then the number of edges in the graph…

A:

Q: Determine the number of spanning trees in graph G that is shown below. Graph G Number of spanning…

A: Let us write the graph by labelling the vertices as,It is clear that the graph is not a complete…

Q: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. 1)…

A: Note: We will be solving Q. 1 only as asked.Given that  and  are two sets of  labeled…

Q: Draw an Eulerian graph which has 5 vertices having one vertex with degree 4 and other vertices with…

A: Given: To draw the Eulerian graph which has 5 vertices having one vertex with a degree 4 and the…

Q: Use Kirchhoff's theorem to find the number of spanning trees for the given graph. Show work.

A: First name the vertices 1,2,3,4,5,6 respectively.

Q: Find the number of spanning trees that can be made of this graph using Kirchhoff's Theorem

A: The total number of spanning trees are given by using Kirchhoff's Theorem

Q: Consider the graph: The graph has an Euler circuit because each vertex has an even degree The graph…

A: Firstly, naming the vertex for better understand.

Q: 14) For each of (a)-(c) below, either draw a graph with the specified properties or else explain why…

A:

Q: Consider the graph with 6 vertices of degree 2, 4, 1,1, 6,3, 5. Does the graph exist? Graph does not…

A: NOTE: As given degree of 7 vertices , so we consider number of vertices as 7 ( otherwise question is…

Q: An undirected graph G with 6 vertices with the degrees 7,3,12,4,4,6 respectively, what is the length…

A: In an undirected graph, an Eulerian path is a path that traverses each edge exactly once. For a…

Q: (10) A graph is connected if, and only if, (Choose one answer from below) A) It consists of a few…

A: A connected graph is graph that is connected in the sense of a topological space, i.e., there is a…

Q: B\ Prove that " there is no simple graph on four vertices, three of whic have degree 3 and the…

A: To prove: There is no simple graph on four vertices, three of which have degree 3 and the remaining…