2. The following table represents a network with the arcs identified by their starting and ending nodes. Draw the network and use the minimal spanning tree to find the minimum distance required to connect these nodes. Arc Distance 1-2 12 1-3 2-3 7 2-4 10 3-4 9. 3-5 4-5 8 11 4-6 5-6 9.

Q: Construct a graph with vertices F, G, H, I, J, K, L that has an Euler path, the degree of L is 1 and…

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Q: How many edges are in this shape?

A: We have to find the edge of the figure.

Q: Construct a graph with vertices P, Q, R, S, T, U, V that has an Euler path, the degree of R is 1 and…

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Q: Draw the network diagram for the above project.

A: Network diagram is drawn by connecting nodes through joining lines.

Q: How many edges does Ks have? Kn in general?

A:

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: construct a graph with vertices Q,R,S,T,U,V,W that has an Euler path and the degree of U is 1 and…

A:

Q: cted edge that has the sr two or more edges have ck anyone.) riving at the next vertex

A: Given as,

Q: 1. Suppose G is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G?

A: Answer :-  a). Suppose G is a planar graph with faces of length 3, 4, 5, 6. How many edges are there…

Q: Construct a graph with Vertices U,V,W,X,Y that has an Euler circuit and the degree of V is 4. What…

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Q: Construct a graph with vertices R, S, T, U, V that has an Euler circuit and the degree of T is 4.…

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Q: R

A: Solution:  Definition of Euler circuit:  A graph has an Euler circuit if and only if the degree of…

Q: Consider the graph given above. Add an edge so the resulting graph has an Euler path (without…

A: An Euler path is a path that uses every edge of a graph exactly once.

Q: Let K, be the complete graph on n vertices. a) Draw Kn for n = 1, 2, 3, 4, 5. For each, how many…

A:

Q: Question 58 There exists a simple graph H with 6 vertices and 7 edges such that H has an Euler…

A: In a simple graph, only one edge exists between any two vertices. Also, each edge starts and ends in…

Q: Construct a graph with vertices M,N,O,P,Q, that has an Euler path, the degree of Q is 1 and the…

A: Euler Path: Eulerian path in a graph is a path that visits every edge exactly once. An undirected…

Q: What is a circuit in the Hamiltonian and what edge can you remove to make a Hamilton path? K1 a (a,…

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Q: Show a Hesse diagram with 5 nodes {1, 2, 3, 4, 5} and 4 edges that has exactly three topological…

A: Given nodes are 1,2,3,4,5 with 4 edges. We know that a topological sorting for a directed acyclic…

Q: 4) Which of the graphs has an Euler path but no Euler circuit?

A: 4. a) Given graph is  We observe that  degree of vertex A, i.e. d(A)=2, d(B)=4, d(C)=2, d(D)=3,…

Q: 9. Obtain the shortest distance and shortest path from vertex 1 to every other vertex in the network…

A: To find the shortest distance between the vertex 1 to every other vertex .

Q: Consider the graph given above. Add an edge so the resulting graph has an Euler path (without…

A: Given-  To find- Consider the given graph above. Add an edge so the resulting graph has an Euler…

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: WHAT is this type of circuit or graph a. Hamiltonian circuit b.Euler path c.Hamiltonian path d.Euler…

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Q: The shortest distance from A to E in the given network is 3 A 1 1 1 C 8.

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Q: 3. Determine the classification of the quadrilateral: Vertices are (0,0), (5,2), (10,10), & (0,6)…

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Q: How many edges are in the Hasse diagram that represents the poset ( {1, 3, 4, 6, 8, 12, 16, 18), I…

A: Solution

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: Hamiltonian circuit,

A: Let the set of vertices of a bipartite graph be V = Vo ∪ V1, where |Vo| = m, |V1| = n and all…

Q: ) The nearest-neighbor tour starting with vertex B is given by:

A:

Q: Construct a graph with vertices I, J, K, L, M, N that has an Euler circuit and the degree of L is 4.…

A: Given that, I, J, K, L, M, N that has an Euler circuit and the degree of L is 4. We have to find the…

Q: Consider the following graphs over the vertices {a, b, c, d, e, f}. Which of them contain Euler…

A: Given- Consider the following graphs over the vertices a, b, c, d, e, f To find- Which of them…

Q: Consider the graph given above. Add an edge so the resulting graph has an Euler circuit (without…

A: Consider the given graph. It has 5 vertices U, V, H, X and T. Also, the number of edges in the given…

Q: Find Euler and Hamilton circuits/paths of this graph

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Q: Question 2: Show that path connectedness is a topological property. Explain and show your work.

A: a property of spaces is a topological property if whenever a space X possesses that property every…

Q: 4. Solve the travelling problem for the given graph by finding the total weight of all Hamilton…

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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: We have to solve given problem:

Q: Construct a simple graph with vertices F, G, H, I,J that has an Euler circuit and the degree of F is…

A: A graph is said to be simple if it has no loops and parallel edges. Degree of a vertex of a graph is…

Q: Construct a simple graph with vertices H, I, J, K, L, M that has an Euler circuit and the degree of…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: K3 Euler path: Euler circuit: Hamilton path: Hamilton circuit:

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Q: Let G be a directed graph with 10 vertices. Let a and b be vertices that are connected by at least…

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

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Q: Construct a simple graph with vertices H, I, J, K, L, M, N that has an Euler circuit and the degree…

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Q: Which of the following sequences of degrees of vertices in a multigraph has a Euler circuit?…

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Q: Construct a graph with vertices U,V,W,X,Y that has an Euler path, the degree of U is 1 and the…

A: We Know that  An Euler path is a path that uses every edge of a graph exactly once.   We have to…

Q: Is it possible for a graph to have both a Euler path and Euler circuit? Explain your answer.

A: Answer :- If a graph has an Euler circuit, i.e. a trail which uses every edge exactly once and…

Q: Construct a graph with vertices I, J, K, L, M, N that has an Euler path, the degree of K is 1 and…

A:

Q: A graph has vertices of degree 1,2,3,3, and 8. How many edges does it have?

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

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…