Give an example of a graph with 5 vertices that does NOT have a Hamiltonian circuit. Explain why not.

Q: If a graph has 5 edges, how many vertices does it have?

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Q: (a) Give the number of edges in the graph.

A: answer is in next step. please give a like !!

Q: Can the following graphs drawn in plane without edge crossings? a

A: Given: Graphs, To determine: Whether the given graphs can be drawn without crossing.

Q: Show that in a simple graph with at least Two vertices there must be two vertices that have the same…

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Q: Draw a simple disconnected graph with 3 vertices.

A: The given problem is related with graph theory. We have to draw a simple disconnected graph with 3…

Q: How many vertices have an even degree?

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Q: Does a Hamiltonian path or circuit exist on the graph below?

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Q: Suppose a graph, G, has five vertices with degrees 9,8,6,5,4. How many edges does G have?

A: We have to find the number of edges in graph G.

Q: 3 Determine whether the graph above has an Euler circuit or Euler trail. Show and prove why is it…

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Q: d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why…

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Q: A graph with four vertices is Hamiltonian if each vertex has a degree of two. True O False

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Q: If a graph has 8 edges, how many vertices does it have?

A: We have to solve given problems:

Q: 5.1. Explain how graphs can be used to model electronic mail messages in a network. Should the edges…

A: # we are entitled to solve only question at a time, please resubmit the other question if you wish…

Q: What is the most edges a graph can have if it has p vertices and has a bridge?

A: Given: A simple graph with p-vertices.

Q: Draw a simple graph with 2 vertices.

A: Solution:To draw a graph with 2 vertices

Q: How many circuits are there in the graph?

A: only two circuis are there.  Which are 2342 and 2432

Q: Construct a simple graph with vertices L, M, N, O, P, Q whose degrees are 1, 2, 4, 3, 4, 2 What is…

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Q: Give an example of a graph with an infinite number of vertices and an infinite number of edges that…

A: A graph consisting of infinite number of vertices and edges is called as an infinite graph.

Q: Suppose that we have a graph with at least two vertices. Show that it is not possible that all…

A: Suppose, we have a graph with at least two vertices.

Q: A graph with eight vertices and seven edges is not connected. True False

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Q: show that a simple planar connected graph with 17 edges and ten vertices cannot be properly colored…

A: We can solve this using Euler theorem

Q: Determine the number of Hamilton circuits in a complete graph with 12 vertices. O A. 121 O B. 11 O…

A: To determine the number of Hamiltonian circuits in a  complete graph with 12 vertices.

Q: If we have two different non-crossing drawings of the same connected graph, is it possible for the…

A: The given question is related with planar graphs. Suppose we have two different non-crossing…

Q: Construct a simple graph that is a forest with vertices B,C, D, E, F,G, H,I such that the degree of…

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

Q: a) graph, 6 vertices, has a Hamitonian circuit and a vertex of degree 3 b) graph connected,…

A: This is a problem of graph theory.

Q: What does the degree of a vertex represent in an academiccollaboration graph? What does the…

A: Definition Used-  In a graph, Degree of a vertex is equal to the number of edges that are incident…

Q: 2) What is the maximum number of edges possible for any bipartite graph between A and B?

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Q: If a planar graph has 18 vertices and 26 edges, how many regions are determined when you draw t…

A: If a connected planar graph G has e edges, v vertices, and r regions, then v-e+r=2. Here,  v=18,…

Q: what is the edge - connectivity in a graph ? And give an example

A: Edge - Connectivity in a graph : Let ‘G’ be a given connected graph.Then the minimum number of edges…

Q: what is the number of edge of Harary graph? explain to me

A: Solution:-

Q: There are _____ number of vertices in a graph 6 edges if each vertex is of degree 3.

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Q: On a Complete Graph with 8 vertices, how many possible Hamiltonian circuit are there?

A: The given graph is complete graph with 8 vertices. It is known that, a complete graph with n…

Q: Explain why it is not possible to draw a planar graph that contains three faces  and the same number…

A: For any planar graph to exist it should satisfy the Euler formula which is given by - v + f = e + 2…

Q: The graph with 5 vertices and four edges is always connected. TRUE OR FALSE

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Q: 10. Describe a graph model that represents whether each employee at a company gathering knows the…

A: According to question given :We have to describe the graph model that represents whether…

Q: Describe a graph model that represents a subway systemin a large city. Should edges be directed or…

A: To sketch: A graph model that represents a subway system in a large city. To check: The edges should…

Q: Draw a graph with two loops around vertex e, with end vertices a and f, with multiple edges on…

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Q: A forest contains 39 vertices and 36 edges. How many connected components does the graph have?

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Q: Draw a complete graph using five vertices a, b, c, d, e.

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Q: A vertex on which no edges are incident is _____.

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Q: The graph with two vertices is Hamiltonian. True False

A: Definition - A graph is Hamiltonian connected if for every pair of vertices there is a Hamiltonian…

Q: Construct a simple graph with vertices N,0, P,Q, R, S whose degrees are 5, 1, 2, 3, 3, 2 What is the…

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Q: Either draw a graph with the following properties, or explain why you cannot: Tree with 9 vertices…

A: We know that, Any tree with n vertices has n-1 edges.

Q: By duplicating only 2 edges, Eulerize the following graph:

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Q: Which graph contains Hamiltonian Path? Hamiltonian Circuit? For those that don’t, give an…

A: We have to find which of the graph contains Hamiltonian Path and  Hamiltonian Circuit

Q: Give an example of a graph on 8 vertices which is i) Hamiltonian but not Eulerian. ii) Eulerian but…

A: A connected graph G is Hamiltonian if there is a cycle in G which covers every vertex of G exactly…

Q: Find a self-complementary graph with 8 vertices.

A: We know the definition of Complement of a graph, The complement of a graph G is a graph G' on the…

Q: What is the number of edges in a tree with 13 vertices?

A: given          there are 13 vertices in a tree          and we have to find numbers of edges in a…

Q: Construct a graph with vertices A, B,C, D, E, F,G that has an Euler path, the degree of G is 1 and…

A: We have to construct a graph with vertices A, B, C, D, E, F, G that has an Euler path, the degree of…