Question: Let G = (V, E) be a simple graph. Let R be the relation on V consisting of pairs of vertices (u, v) such that

Let G = (V, E) be a simple graph. Let R be the relation on V consisting of pairs of vertices (u, v) such that there is a path from u to v or such that u = v. Show that R is an equivalence relation.

Step by Step Solution

★★★★★

3.48 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The definition given here makes it clear that u a... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

923-M-C-M-S (2362).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let G be a simple graph. Show that the relation R on the set of vertices of G such that uRv if and only if there is an edge associated to {u, v} is a symmetric, ir-reflexive relation on G.

Let G = (V, E) be a loop-free connected graph with | V | = v. If | E | > (v/2)2, prove that G cannot be bipartite.

Let G = (V, E) be an undirected graph with subset I of V an independent set. For each a I and each Hamilton cycle C for G, there will be deg (a) - 2 edges in E that are incident with a and not in C....

Let G = (V, E) be a directed graph with weight function w : E R, and let n = |V|. We define the mean weight of a cycle c = e 1 , e 2 , . . . , e k of edges in E to be Let * = min c (c), where c...

Question 9 (3 points): Let G = (V, E) be a simple directed graph in which every vertex u has a real weight wu). For each vertex u, let Min Weight(u) = min{W(): reach(u), where reach() is the set of...

I have already done part i). You can take it as a fact for part iii). Question 9 (3 points): Let G = (V, E) be a simple directed graph in which every vertex u has a real weight wu). For each vertex...

Let G = (V, E) be a simple directed graph in which every vertex u has a real weight wu). For each vertex u, let MinWeight(u) = min{w(2): reach()}, where reach() is the set of vertices v EV reachable...

Let G = (V. E) be an undirected graph with all edge weights equal to I. Let d(i, j) denote the length of the shortest path between i and j. Now, suppose we wish to answer queries from the user of the...

Let G = (V, E) be a directed graph where V = { 1,2, . . . ,n} such that n is odd; Le n = 2k+1 for some k > 0. Given a vertex v, let TO, be the set of all vertices from which there is path to v. Let...

Let G = (V, E) be an undirected graph with no parallel edges. A 2-edge-colouring of G is an assignment of a colour 'red' or 'blue' (for short r and b) to each edge of G. Let c : E {r, E be a...

a. Use the method of Lagrangian multipliers to solve Problem 12. b. Do you get the same response as you do without using this method? c. What does equal? What does this mean?

Nature Food Inc. needs to estimate the cost of financing on preferred stock. The firm has preferred stock outstanding that pays a constant dividend of $3.44 per year. That preferred stock is...

15. LO.3 The Flan Trust is scheduled to terminate in two years, when Amy Flan reaches age 30. Several years ago, the trust operated a business that generated a sizable NOL carryforward that the trust...

A monopolist wishes to increase profits, and so he begins an advertising program that features a giveaway-a free ball point pen is given away with each purchase in an attempt to stimulate demand....

Use the Chain Rule to prove the following. (a) The derivative of an even function is an odd function. (b) The derivative of an odd function is an even function.

(a) Use differentials to find a formula for the approximate volume of a thin cylindrical shell with height , inner radius , and thickness r. (b) What is the error involved in using the formula from...

(a) If is a positive integer, prove that (b) Find a formula for the derivative of y = cosnx cos nx that is similar to the one in part (a). (sin"x cos nx) n sin"-'x cos(n + 1)x dx

Massey Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $440,000 is estimated to result in $175,000 in annual pretax cost savings....

i need help solving this problem personal scanner to create the PDF. In a random sample of 50 cross-country runners, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.12....

Required information [The following information applies to the questions displayed below.) Brodrick Company expects to produce 20,400 units for the year ending December 31. A flexible budget for...