Show that the average degree of a vertex in the triangulation is strictly less than 6.

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: 2.) Determine how many backtracks are required to use every edge at least once returning to where…

A:

Q: Of all rectangles with given area, A, which has the shortest diagonals? A rectangle with area A has…

A: Dimention are : A×A

Q: How many cut vertices does the path Pn has for n ≥ 1?

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Q: find the minimum Hamilton circuit from the table starting at G. 10 10 12

A: Given The given table is Nearest Neighbor Algorithm→ i) Pick a starting vertex. ii) select the…

Q: Show that the maximum number of edges in a graph with n-vertices is *C2 (d)

A:

Q: Show that if n > R(6,6) and we partition the edges of the complete to 4 pieces then one of the…

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

Q: 17. Find a path from A to A that passes through each edge exactly one time. If none exists explain…

A: An Euler circuit is a circuit that uses every edge of a graph exactly once and its starting and the…

Q: Show that multiplication of two Dedekind cuts in ℝ ≥0 is commutative and associative.

A: Let us take that the two cuts are α and β . Confine these to ℝ+, the set of all α∈ℝ with α>0*.…

Q: 4. Prove the following theorem: If a graph has more than two vertices of odd degree, then it does…

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Q: In how many ways can one walk from A to B by taking the shortest possible path along the grids?

A: In this case, we are able to move up or right. From the diagram we can move 4 rights, and 5 ups'.

Q: on Find the largest number of paths from 4 to B that do not have any edges in common.

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Q: 6 16 -12-

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

A: Rooted TreesA rooted tree is a tree in which one vertex has been designated as the root and every…

Q: Draw a diagram of the factors limiting maximal running performances of 1500 m to 5 km.

A: Draw a diagram of the factors limiting maximal running performances of 1500 m to 5 km.

Q: Find the sum of the degrees of the vertices of each graph in Exercises 1–3 and verify that it equals…

A: Given graph is

Q: Suppose we are told that a connected graph cuts the plane into 211 regions. How many more edges than…

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

A: The level of a vertex v in a rooted tree is the length of the unique path from the root to this…

Q: Prove the inequality theorem 6 which states that the sum of the lengths of any two sides of a…

A: Consider a triangle ABC as shown below.

Q: What is the Pru fer code for a simple path whose vertices are numbered in increasing order (i.e., 1…

A: The complete solutions are given below

Q: At Lana's bake sale, 2/3 of the brownies were purchased by 5/7 of the customers. If there were at…

A: Let X be the number of brownies and Y be the number of customers. It is given that 2/3 of the…

Q: Use the pigeonhole principle to prove that a graph has at least two vertices with the same degree

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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: The of a vertex is the number of edges along the unique path between it and the root . Child Degree…

A: Here we are given the definition from graph theory. We have to fill the blank with appropriate word…

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

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Q: Find the maximal area of a right triangle with hypotenuse of length 1

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Q: IFA and B have 6 and 9 elements each, what is the minimum number of elements Aunion B?*

A:

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

A:

Q: Let P be a path graph with n2 4 vertices. What is the length of a longest path in the complement of…

A: In the given question, concept of graph theory is applied. Graph Theory A graph is a figure made up…

Q: This refers to the number of edges incident to a particular vertex. Answer:

A: Explanation of the answer is as follows

Q: Show that of all n-gons having the same perimeter, the regular n-gon has the greatest area.

A: All n-gons having the same perimeter

Q: 6- Find the areas of the triangles whose vertices are given in А(-1, -1), В(3, 3), С(2, 1)

A: We will solve the problem.

Q: In ANOP, mZN = 110° and mZO = 38°. Which list has the sides of ANOP in order from longest to…

A: Given that, m∠N=110°, m∠O=38° in ∆NOP

Q: If a graph with six vertices is embedded in S?, what is the maximum number of edges it can have.…

A: Consider the provided question, A graph G is embedable on S2 if it is embedable on a plane. Since,…

Q: Sketch the region that corresponds to the given inequalities, say whether the region is bounded or…

A: We consider the corresponding equation and draw third graphs. Then we find the area bounded by the…

Q: It is obvious that for a bipartite graph to contain a perfect matching, it is necessary that |A| =…

A: Given That: It is obvious that for a bipartite graph to contain a perfect matching, and also it is…

Q: Show that the number of planted plane trees on n vertices, m of which are leaves (that is, have zero…

A: Solution

Q: (a) How many vertices does it have? (b) How many lateral edges does it have? (c) How many base edges…

A: First we will draw a nonagonal prism

Q: What is the minimum number of faces a prism can have?

A: Given: What is the minimum number of faces a prism can have?

Q: What is the minimum of the costs of the spanning trees in the network shown? 7 8 3 LO

A: Let us label the vertices of the given graph as follows:

Q: Find the sum of the degrees of the vertices of each graph in Exercises 1-3 and verify that it equals…

A: We know that, Degree of vertex is the number of edges passing through that vertex. We need to…

Q: Prove that the sum of the degrees of the vertices of any finite graph is even.

A:

Q: Given an undirected network of N > 1 nodes which is connected. Which is the maximum diameter?

A: As given by the question There are given that the N>1 connected nodes. According to the maximum…

Q: A vertex is pendent if its degree is zero. True false

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Q: Prove that Complement of a bipartite graph need not be a bigraph

A: Bipartite graph ⇒ A bipartite graph is a graph whose vertices can be divided into two disjoint and…

Q: 5. Can somcone cross all the bridges shown in this map cxactly once and return to the starting…

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Q: Suppose that we have free segments with sizes: 6, 17, 25, 14, and 19. Place a program with size 13KB…

A: Given: Free segments with sizes: 6, 17, 25, 14, and 19 Here, it has been asked to place a program…

Q: Construct a connected simple graph, that has no circuit, with vertices M, N,0, P, Q, R, S, T, U such…

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Q: . Which complete bipartite graphs Km,n, where m and n positive integers, are trees? are

A: