Question 1 Tell whether the following graphs exist. If they exist, draw the graph. Graph, three vertices, two edges, not a tree. Graph, circuit-free, seven vertices, four edges. Graph, connected, nine vertices, eight edges, has a circuit. Tree, five vertices, total degree 10. Tree, twelve vertices, fifteen edges.

Q: QUESTION 14 Total number of edges of a complete graph which has 9 vertices is None 36 edges 12 edges…

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Q: How many vertices do the following graphs have if they contains a) 16 edges and all vertices of…

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Q: Question 3 Draw a diagram representing the graph with the following vertices and edges V = {A, B, C,…

A: A graph is defined as a mathematical figure of a network and it shows the relationship between lines…

Q: Question 1 The total degree of a graph is the sum of the degrees of all the vertices. What is the…

A: The total degree of the graph is sum of the degrees of all the vertices. Degree of a vertex is the…

Q: Question 2 Show that if n > R(6,6) and we partition the edges of the complete graph K, into 4 pieces…

A: According to the given information, it is required to show that:

Q: E FO Figure 1

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Q: A graph with 8 vertices has degrees 1, 1, 2, 3, 5, 7, 8, and 9. How many edges does it have?

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Q: Which of the graphs has 4 as its chromatic number? a. graphs 1 and 2 only b. graph 2 only c. graph…

A: Definition: Chromatic number is a number of minimum colours needed to colour the vertex of the given…

Q: QUESTION 5 Consider the set y =ta.b.c.d. e) to answer the questions below. Please, do not write your…

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Q: 8. Please find the vertex and edge sets of the following graph Vy ez ez

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Q: VI el es e2 eq S U2 e3 V5 e6 VA FIGURE 1 eA es V3 V9. Ug Vo V5 VI V7 FIGURE 2 VA V6 V2 V3

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Q: Question 1 a. Are all circuits also paths? Do not just answer yes or no, but briefly explain why. b.…

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Q: Suppose a graph G has 1E-23, sax vertices of degree 4, five vertices of degree 3 and the rest have…

A: Given below the detailed solution.

Q: Question 2 Show that if n > R(6, 6) and we partition the edges of the complete graph Kn into 4…

A: According to the given information, it is required to show that:

Q: The graph G has 5 vertices with degrees 2, 3, 3, 4, 4 . How many edges does G have? edges Could G be…

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Q: The first floor plan of a commercial building is shown at the right. Draw a graph (with complete…

A: Answer is mentioned below

Q: In which of the following graph can red or blue be assigned to the vertices such that no two…

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Q: Draw a graph that represents this information, where each vertex represents a phone company and an…

A: Graph drawing

Q: How many cycles of length 4 (i.e. 4 edges) are in the complete graph Kg? Note: the cycle 1-2-3-4-1…

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Q: Consider the following graph. B C F Find the degree of each vertex. deg(A) deg(B) deg(C) deg(D)…

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

A: From drawing the graph it is clear.

Q: QUESTION 3 The number of edges in a tree with 16 vertices is O At least 15 O At most 15 O Possible…

A: To find the number of edges in a tree with 16 vertices

Q: Figure 1 (a) and Figure 1 (b) show a connected graph of six different vertices.   find the least…

A: Given that : By the definition of the connected graph , If there is a path exists between every…

Q: 8. Which one of the following statements is NOT true about this graph? B E F Figure 1 OA) There is a…

A: Definition: This is a circuit because a path which ends at the vertex it begins. Given graph is…

Q: QUESTION 14 A simple graph that contains exactly one edge between each pair of distinct vertices is…

A: A complete graph is a graph in which each pair of graph vertices is connected by an edge.

Q: Consider the following graph: B E How many vertices are there? How many edges are there? What is the…

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Q: Consider the following graph that represents Facebook "friends": Joe Bill Jose Amit Mary Find the…

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Q: 4. How many edges in the union of the graphs in Fig.1 and Fig.5? a) 25 b) 23 c) 21

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Q: 20. Suppose we are given the following graph V3 V4 Us V7 V2 V1 a) Find an Euler circuit. b) Does the…

A: Euler Circuit: An Euler circuit is a circuit that uses every edge in a graph with no repeats. Being…

Q: QUESTION 15 The of a vertex is the number of edges along the unique path between it and the root.…

A: The level of a vertex is the number of edges along the unique path between it and the root.

Q: QUESTION 20 For the following graph, which statement is true? There is an Eulerian circuit. More…

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Q: In a connected planar graph drawn with no intersecting edges, if there are 3 vertices and 8 edges,…

A: We can use the Eulers formula for the planar graph to find the number of faces.

Q: 1? In the following graph, how many vertices are there in the degree 1.5 egocentric graph centred on…

A: Given 1.5 egocentric graph. From the graph: Total number of nodes in the graph=12. Number of…

Q: Each graph and explain why the graph does or does not have an Euler circuit. If it does, specify the…

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Q: 5. A a) complete graph b) subgraph c) line graph d) bar graph can be on a non-planar graph.

A: According to our guidelines , we can answer only first question . Kindly re-post other questions .

Q: Model the following problem into a graph coloring problem: Each of the following five committees…

A: Given: Committee A={Smith, Jones, Brown, Green} Committee B={Jones, Wagner} Committee C={Harris,…

Q: Given two graphs below: D. a) Find min size edge coloring of each graph? b) prove a proof that no…

A: Given two graphs.

Q: Question 8 Consider the following graphs, each with vertex set V = {1, 2, 3, 4, 5, 6}, G1 = (V, E1),…

A: The given question is related with graph theory. Consider the following graphs, each with vertex set…

Q: San Francisco $45 L.A. $100 $45 $25 $75 $80 Denver $20 Chicago Dallas $90 San Diego How many edges…

A: Solution

Q: 1) Is the graph in Fig.1 a) a connected graph? b) a complete graph? c) a tree? d) a weighted graph?…

A: Questions from graph theory.

Q: Question 1. Which of the following graphs are trees? "M d) f)

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Q: Which of the following edges do we need to add to make the following graph ergodic? 3 4 O 2->3 O…

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Q: Consider the following graph. B D F Find the degree of each vertex. deg(A) deg(B) deg(C) deg(D)…

A: We will use the definition of degree of a Undirected Graph and Euler Circuit and theorem which…

Q: A graph has 10 vertices - 6 vertices of degree 3, 2 vertices of degree 4, and 2 vertices of degree…

A: See the detailed solution below.

Q: 2. A graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges does the graph have?

A: The Handshake theorem states that the sum of the degrees of the vertices of the graph  (that is, the…

Q: Answer the following questions based on the given graph. B D. E F H. Number of vertices of the given…

A: A graph is given. We need to answer the given questions based on the given graph. The solution is…

Q: QUESTION 16 For the following graph, which statement is true? O There is no Eulerian path or…

A: This is a problem related to graph of the eulerian theory. Please follow the procedure given below.…

Q: QUESTION 14 A graph has 5 vertices: two vertices of degree 3, a vertex of degree 2, a vertex of…

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Q: 10.  For each of the following, draw the graph or explain why the graph cannot exist: (c) A…

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Q: 12. How many miles will be traveled by at least 50% of the trucks? (Hint: Draw a graph.) ilidadong…

A: GivenMean(μ)=50.0standard deviation(σ)=12.0