There is no formula for the number of nonisomorphic trees on n vertices. But there is one for labeled trees! Using Prüfer sequences, prove Cayley’s Formula, that the number of distinctly labeled trees on n vertices is n^(n-2).

Q: 20. Three jealous wives and their husbands come to a river. The party must cross the river (from…

A: Given- Three jealous wives and their husbands come to a river. The party must cross the river (from…

Q: How many ternary ( 0,1,2) sequences of length 10 are there without any pair of consecutive digits…

A: We need to find the number of ternary(0,1,2) sequence of length 10 are there without any pair of…

Q: Enter the number to complete the linear combination. gcd(80, 35) yields sequence: 80 35 10 5 0 10 =…

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Q: A graph has degree sequence (4, 4, 1, 1, 1, 1, 1, 1). How many such graphs are there, up to…

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Q: c) Find the Graph whose adjacency matrices is given by 0|1|0|0 |0 10 10 10 010|1 0|1|0|1| 1 |0…

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

Q: (c) Find the Graph whose adjacency matrices is given by 0|0|0|0 10|1|0| 1|0 0|10|1| 1|0 00|1|0| 1 |0…

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

Q: 5. List the first 10 terms of each of these sequences. a) the sequence that begins with 2 and in…

A: Since you have posted a multi subparts question according to guildlines I will solve first(a,b,c)…

Q: 4. Construct all degree sequences for graphs with four vertices and no isolated vertex.

A: Construct all possible degree sequences with four vertices and no isolated vertex

Q: How many ordered sequences are possible that contain four objects chosen from thirteen?

A: According to the given information in this question We need to find the value P( 13,4)

Q: (25p) Provide a simple formula or rule that generates the terms of an integer sequence that begins…

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Q: Q2// a) A graph has 16 edges, 5 vertices of degree 4, and the other vertices of degree 2. How many…

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

Q: Find at least three different sequences beginning with the terms 1, 2, 4 whose terms are generated…

A: A sequence is an enumerated collection of objects in which repetitions are allowed and order…

Q: Suppose that n objects are to be colored with red, yellow, green and blue in a way that both green…

A: Given: Number of objects, i.e. n, and color used for coloring that object, i.e. red, yellow, green,…

Q: Let a_n be the number of graphs in which the degree of each vertex is 2 and the number of vertices…

A: D(x)is supposed to be the exponential generating function for the number of connected graphs on n…

Q: This is from a linear algebra book A sequence {a,}-o is defined recursively as follows n=0 ao = 0,…

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Q: Explain why there are no simple graphs with these degree sequences. (а) 6,6,5,3,2,2,2 (b)…

A: a) Given degree sequence is        6,6,5,3,2,2,2 We prove there is no simple graph with this degree…

Q: 3. Using Bubble sort, sort the following values in an increasing order. 8,2,4,9,12,7,10

A: Given data is : 8,2,4,9,12,7,10

Q: ppose a graph G has the following degree sequence: 5,5, 4, 3, 3, 3, 1 en the graph G has vertices…

A: To find the number of vertices and edges we need to look into the question.Here given thar there is…

Q: Use induction to prove the theorem: A tree with n vertexes has n-1 edges.

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Q: Give a recursive definition of the sequence 2, 4, 6, 8, 10, . Then write the corresponding recursive…

A: Given sequence is 2, 4, 6, 8, 10, .......... We have to write the corresponding recursive algorithm.…

Q: Help in Discrete Structure (Math) 23(i). Using mathematical induction method, prove that the sum of…

A: Using mathematical induction method, prove that the sum of first n positive integers is n(n+1) /2

Q: Use a tree diagram to find the number of ways 2 letters can be chosen from the set (P,Q,R} if order…

A: Number of letter=3 Number of letter to choose=2 (a) When repetition is allowed then number of…

Q: labelled tree has the Prufer sequence (2, 4, 6, 5, 3, 1, 2). Determine the maximum degree of a…

A: To give the answer to the question we have to find the maximum degree of a vertex in the tree and…

Q: Is there a degree sequence such that the graph can only be drawn as a simple graph but not a…

A: Yes. There is a degree sequence such that the graph can only be drawn as a simple graph but not a…

Q: Does the following sequence of integer numbers [6,6,5,4,3,3,1] correspond to a degree sequence of a…

A: here we consider the fact about the degree and number of edges of graph and tree.

Q: 6. A bit string is a finite sequence of 0's and 1's. (a) How many bit strings have length 12? (b)…

A: Since you have posted multiple questions but according to guidelines we will solve first question…

Q: How many edges does a tree with 10000 vertices have?*<

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Q: Give an efficient algorithm that, for any sequence d₁, d2, ..., dn that is th sequence of a tree,…

A: Here is an efficient algorithm that constructs a tree from a degree sequence: Sort the degree…

Q: Devise a recursive algorithm to find the nth term of the sequence defined by a = 1, a₁ = 2, and a =…

A: We can use a recursive algorithm to find the    n-th term of the sequence defined bya0 = 1, a1 = 2,…

Q: Determine whether the sequences are a degree sequence of a simple graph on five vertices. If it is…

A: Ans- (i) (3, 3, 3, 3, 2) This is a valid degree sequence of a simple graph on five vertices. One…

Q: Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the…

A: The general formula that is given for drawing different things with replacement and with the order…

Q: find the sum of all even intergers less than 1000 that are exactly divisible by 7

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.