Prove that a tree with n vertices has n - 1 edges, Mathematics

Assignment Help:

Prove that A tree with n vertices has (n - 1) edges.   

Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should be (n - 1) incoming arcs to the (n - 1) non-root nodes. If there is any another arc, this arc should be terminating at any of the nodes. If the node is root, after that its indegree will become one and that is in contradiction along with the fact that root all time has indegree zero. If the end point of this extra edge is any non-root node after that its indegree will be two, which is once again a contradiction. Therefore there cannot be more arcs. Hence, a tree of n vertices will have exactly (n - 1) edges.


Related Discussions:- Prove that a tree with n vertices has n - 1 edges

Determine coefficient of traction, Problem 1 Work through TALPAC 10 Bas...

Problem 1 Work through TALPAC 10 Basics (refer to attached handout). Answer the set of questions at the end of tutorial module. Problem 2 Referring to both the haul cyc

Complex numbers from the eigenvector and the eigenvalue, Complex numbers fr...

Complex numbers from the eigenvector and the eigenvalue. Example1 : Solve the following IVP. We first require the eigenvalues and eigenvectors for the given matrix.

Find out the product of 5.2 × 10^3 and 6.5 × 10^7, Find out the product of ...

Find out the product of 5.2 × 10 3 and 6.5 × 10 7 . Write your answer in scientific notation. To multiply numbers written within scienti?c notation,  multiply the ?rst numbers

what fill amount are they searching, Brewery has 12 oz bottle filling mach...

Brewery has 12 oz bottle filling machines.  Amount poured by machine is normal distribution mean 12.39 oz  SD 0.04 oz. Company is interested in in reducing the amount of extra beer

Math Help, 1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x ...

1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x 10^9 b. 3.2 x 10^9 c. 5.3 x 10^9 d. 7.4 x 10^8 2. Which of the following is less than 6.5 x 10^-5 a. 1.4 x 10

Rounding decimals, i need help rounding decimals to the nearest 100th and t...

i need help rounding decimals to the nearest 100th and tenth

Show that the angles subtended at the centre , A circle touches the sides o...

A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

What is the square root of -i and argument of -i, What is the square root o...

What is the square root of -i and argument of -i Ans) argument of -i is 270 ad 1 is the square root of -i

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd