(a) Show that the number of vertices in a binary tree is odd. Also calculate the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(a) Show that the number of vertices in a binary tree is odd. Also calculate the forinula for the number of pendant vertices in a binary tree. (b) i. Find the minimal spanning tree in the graph shown in Figure 4, where the weight of the each edge is also given in the graph. ii. Find all the fundainental cut sets corresponding to the ininimal spanning tree. iii. Express the cut set {e, f, k, l} as ring sum of the fundamental cut sets obtained in part (ii) above. b.4 e.6 h.8 d.3 9.7 i2 1,8 k.5 Figure-4 (a) Show that the number of vertices in a binary tree is odd. Also calculate the forinula for the number of pendant vertices in a binary tree. (b) i. Find the minimal spanning tree in the graph shown in Figure 4, where the weight of the each edge is also given in the graph. ii. Find all the fundainental cut sets corresponding to the ininimal spanning tree. iii. Express the cut set {e, f, k, l} as ring sum of the fundamental cut sets obtained in part (ii) above. b.4 e.6 h.8 d.3 9.7 i2 1,8 k.5 Figure-4
Expert Answer:
Answer rating: 100% (QA)
4 First rt Every binry tree hs n dd number f verties rf rt frm the rt every ver... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
Students also viewed these mathematics questions
-
Show that the number of labeled trees with n vertices, k of which are pendant vertices, is (n - k)!S(n - 2, n - k) = (n!/k!)S(n - 2, n - k), where S(n - 2, n - k) is a Stirling number of the second...
-
In Exercise determine the number of vertices and edges and find the in-degree and out-degree of each vertex for the given directed multi-graph. a
-
For n Z+, show that the number of partitions of n in which no even summand is repeated (an odd summand may or may not be repeated) is the same as the number of partitions of n where no summand...
-
When working as a tax professional, one issue that often arises is the need to provide difficult or disappointing guidance to a client. In the following example, determine the best course of action....
-
Write each of the following condensed structural formulas as a bond-line formula: (a) (CH3)2CHCH2CH3 (b) (CH3)2CHCH2CH2OH (c) (CH3)2C==CHCH2CH3 (d) CH3CH2CH2CH2CH3 (e) CH3CH2CH(OH)CH2CH3 (f) CH2...
-
What is the difference between "low end" and "high end" disruptive innovations?
-
An experiment consists of five draws from a pack of cards. Denoting the outcomes BRRBR, BRRRB,..., for black and red cards and assuming that all 32 outcomes are equally likely, find the probability...
-
The following information describes the companys sales for the year: (a) A sale for $100,000 was made on March 23. As of the end of the year, all work associated with the sale has been completed....
-
(a) Identify and describe current trends or socio-economic situations in the marketing an environment that will influence consumers to adopt or not adopt this product in the near future, in the next...
-
Using Stellarium Web, change your location to the town of Auvers-sur-Oise by pasting 49.070720, 2.169886 into the location search box. Next, change your observing date to 1890-06-16. Look to the West...
-
An unknown wire in a circuit has a circular cross-section with diameter 2.5 mm. It carries a current of &.7 mA. Part (a) What is the current density, in milliamperes per square centimeter, in this...
-
How do partnerships and collaborations with external stakeholders, including community organizations, advocacy groups, and industry associations, enhance organizations' capacity to advance diversity,...
-
What is the name of the technique the Ancient Greeks used to cast bronze statues?
-
On January 1, 2023, Cunningham Corp. is preparing to issue $2 million of five year term bonds (due January 1, 2028) with a 5% stated interest rate and semiannual interest payments. However, it finds...
-
How do global trends, such as demographic shifts, migration patterns, and geopolitical dynamics, influence the imperative for diversity and inclusion within multinational corporations and global...
-
Property valuation reliance on experts a firm of real estate value, to perform a valuation of all real estate held by the company. As a result of this revaluation, property values on the balance...
-
In 1889, Vincent Van Gogh's painting "Sunflowers" sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, what...
-
According to a New York Times columnist, The estate tax affects a surprisingly small number of people. In 2003, . . . just 1.25 percent of all deaths resulted in taxable estates, with most of them...
-
Let E = {, x, y, z} where P denotes a blank, so x x, P, and x xy but xy = xy. Compute each of the following: (a) |||| (b) || || (c) |||| (d) || || (e) || 3 || (f) ||xy|| (g) |||| (h) ||10||
-
(a) Let G = (V, E) be a loop-free undirected graph. Recall that G is called self-complementary if G and are isomorphic. If G is self-complementary (i) determine |E| if |V| = n; (ii) prove that G is...
-
Show that when any edge is removed from K5, the resulting subgraph is planar. Is this true for the graph K3,3?
-
Why can staging investment decisions add value?
-
How do you use a decision tree to make the best investment decision?
-
How can you identify a real option in a decision tree?
Study smarter with the SolutionInn App