HELP needed on HW Questions ASAP Discrete Mathematics: 5. For each of the following, either draw the graph or prove that there are none: a) A graph with 8 vertices, whose degrees are 2,2,2,3,2,2, 1, 2. b) A simple graph with degrees 1,2,2,2 c) A tree with 12 degrees

Q: Consider the star graph ?? of order n, n-star, which is a tree on n vertices with 1 vertex having…

A: Given Sn is the star graph. According to Bartleby the solution to the first three questions is given…

Q: QUESTION 19 Choose the true statement for the following graph. A C D E a. The graph has an Euler…

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Q: 4. Consider the following graph. ez es a. How many paths are there from v to vy? b. How many trails…

A: Image is attached with detailed solution.

Q: Answer the following questions: a.Suppose that a connected bipartite planar simple graph has e…

A: "Hey ,since there are multiple questions posted, we will answer first question. If you want any…

Q: A Triangle Graph, Tn, is a graph where there are n vertices beside each side of a triangle. Thesen…

A: If n is the number of vertices in a graph,Then the number of edges is C2n=n(n-1)2…

Q: Find the chromatic number of each of the following graphs. Give a careful argu- ment to show that…

A: Let the colors be labelled as 1, 2,3, ... . To find the chromatic number, assign color to the…

Q: Consider the following figure: a. Input the degree number for each vertex Vertex Degree Vertex A…

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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:

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Q: Consider the two following graphs and denote the upper graph as G and the lower graph as H. Answer…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 15. (a) Suppose a graph has 5 vertices and 7 edges, and every vertex has degree 2 or 3. How many…

A: The handshaking theorem states that the sum of the degrees of all vertices in a graph is twice the…

Q: a) What is the degree of the graph?  (b) All the vertices have  degree and so this graph has an…

A: The degree of the vertices are as follows degree of A= 2 Degree of B =4 Degree of C=4 Degree of D =…

Q: Let G be a (p, q) graph. Prove that the sum of the degrees of the vertices of G equals twice the…

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Q: John Joe Jean Jane Jenny Kenny Bil Ben Fig. 1.17 1.4 Draw a graph corresponding to the family tree…

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Q: If a complete graph has degree 3 for each vertex, then how many diagonals are in the graph? * 2 O 5

A: Given graph is complete and each vertex has degree 3.

Q: What is the chromatic number of (i) each of the Platonic graphs? (ii) the complete tripartite graph…

A: As assignment of colors to a graph’s vertices such that no two adjacent vertices share the same…

Q: What is the degree of vertex  E ?     (b) List all the even vertices and all the odd vertices.…

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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: The complete bipartite graph K_(n,m) has chromatic number two..* false O True

A: Remark: The chromatic number of a graph G is the smallest number of colors needed to color the…

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 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: The number of edges in a graph with 12 vertices each of degree 6 is O 72 O 1 O 12 O 36

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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: 1. The vertex which is of 0 degree is called? O Internal node O Leaf O Root O None of the above

A: Vertex

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

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Consider the following. (a) Give the number of edges in the graph. | edges (b) Give the number of…

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Q: Is there a simple graph on 5 vertices such that all have distinct degree? 1.If so, draw one. If not,…

A: 1. Consider the given statement "Is there a simple graph on 5 vertices such that all have distinct…

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: Given fean + 2 Draw a graph and clearly show the araph's inter cepts and the axes off Symmetry

A: Topic:- function

Q: O Let G be a such that graph with 10 verti ces 8CG) = ACG) = 2 How many edges does G have?

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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: 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 graph G in Fig. 8-58. Find: (a) degree of each vertex (and verify Theorem 8.1); (b) all…

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Q: Consider the following statements: S: There exists a connected simple graph with 6 vertices and 5…

A: We have to verify the given statements.

Q: An te gr a) Draw K, for n = 1,2,3,4,5. For each, how many edges are there?

A: a)

Q: 1. Which of the next sets establish a bipartition of the graph in Fig.1? a) {a, h, g, b, f } and {i,…

A: Graph has an odd cycle which is a-e-c-a And if a graph contains odd cycle can not be bipartite.

Q: 1. Define the following : Graph Trail iv) k-regular v) Bigraph i) ii) iii) Girth

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: The number of edges in a graph with 8 vertices each of degree 7 is O 7 O 56 28 O 14

A: We have to solve given problem:

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: (a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de- gree 2. This…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

Q: Explain why the graph shown to the right has no Euler paths and no Euler circuits. A D H. Choose the…

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Q: Consider the following. (a) Give the number of edges in the graph. edges (b) Give the number of…

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Q: Consider the star graph Sn of order n, n-star, which is a tree on n vertices with 1 vertex having…

A: Given Sn is a star graph. We need to  c) find the chromatic number of Snd) represent S5 with an…

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: Find the chromatic number of each of the following graphs. Give a careful argument to show that…

A: The given graph is:

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

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Q: .Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can…

A: Sum of the degrees is 4+1+5+3+4+3=20, which is even. So H is a graph. Therefore, option C is not…

Q: 19. (a) For which values of m and n is the complete bipartite graph Km.n a tree? (b) For which…

A: please see the attachment

Q: How many vertices will the following graphs have, if they contain: (a) 18 edges and all vertices of…

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