Graph Definition and 998 Threads

Please check if my two following proofs are correct. I didn't know whether it was better to post them in a separate thread or not. I posted them together since they are both questions related to graph theory. Let me know if I should have separated them. Prove that a graph G is a tree iff it has...

Prove that a graph on v vertices that has no cycle is connected iff it has precisely v-1 edges. Necessary Condition: A connected graph with no cycles is a tree. Therefore, it has v-1 edges. Sufficient Condition: I need help with this. How can I use "a connected graph has no cycles iff it has...

Here is the graph in question: The edges in red are the paths that must be included in the cycle, since vertices a, k, e, and o have only degree 2. I listed all possible routes starting from vertex b, and showed that they all routes closes a cycle while leaving some vertex disconnected. Is...

[SOLVED]Graph theory proof The graph G has precisely two vertices x and y of odd degree. A new graph of multigraph H is formed from G by adding an edge xy. If H is connected, prove that G is connected. Please check my following proof for this problem. Since G has exactly two odd vertices...

need help with this question, is the gradient negative or positive since the voltmeter is over the battery? Here is the image (sorry for making you tilt your heads) https://www.dropbox.com/sh/v6ydqbfrg20whtb/ZWR-r9ZOSH?lst#f:q17.JPG

Hi guys, so I've never used MATLAB before, and i need to make a plot that changes constantly. Let's say that i have Sin(x) from 0 to 3pi Then i need it to change to a Cos(x) from 0 to 3pi then to a Tan(x). I could do it in other languaje like Php or c, but in MATLAB i have no idea. I...

Homework Statement Well I think the answer is d because if the acceleration is constant then the distance should increase at a steady rate hence the straight line for d. But my teacher says different his working is shown on the side of the question. He believes the answer is A...

I have fairly simple non linear graphs that I need equations for. Sometime back I used a program that gave me a power series equation when multiple cordinates of the graph were entered. I no longer have that program and don't remember where I got it. How Can I get these equations? There must...

Homework Statement See code below: The Attempt at a Solution I am simply trying to get the code to work: When I try to compile, the terminal says that apparently the package ptolemy.plot.* package does not exist and so does not recognise statements like PlotFrame etc.. Why is this...

Quick question guys.. I understand how trig graphs work (cos, sin, tan etc.). What I don't understand is when there is a horizontal translation of say, pi/4, I notice that the graph moves, but I don't really understand how to know exactly how far to move. For example if your HT was pi/4 and...

Someone showed me a graph that has to do with how a cylinder oscillates in uniform flow, starting from no oscillation, to high oscillation, back to none. I know the y-axis is amplitude/diameter and the x-axis is velocity / (natural frequency X diameter) I would just like to find out more...

Homework Statement Find the points on the graph of y = x3ex where the tangent line is horizontal. (Your answer should include x-values and y-values) Homework Equations Product rule fg'+gf' The Attempt at a Solution (x3)(ex)+(ex)(3x2) x3ex+3x2ex= y' x3ex+3x2ex= 0...

So I have a function which represents motion. This function is x^2 which is also the area of a square. Now, what I know from the calculus is that the derivative is 2x, no arguing there but the derivative of a squares area is the perimeter, which is 4x? 4x and 2x are not the same at all! Another...

Homework Statement Find a polar equation with the graph as xy=16 Homework Equations r = ed/(1+- cos\theta)? I'm not really sure at all. The Attempt at a Solution I also tried using x = rcos\theta and y = r sin\theta but I can't get anything. I know it's a hyperbola.

Homework Statement A particle starts from rest and accelerates as shown in the attached figure. Determine (a) the article's speed at t=10s and t=20s. (b) The distance traveled in the first 20s. Homework Equations a=dv/dt The Attempt at a Solution (a) t=10s, speed = 20m/s t=20s...

In the graph of volume against 1/pressure,why does the straight line graph not touch the starting point. Whereas,in the graph of pressure against 1/volume,why does the straight line graph touch the starting point?? Thanks. Pls helppp!:)

Homework Statement I know this is the description of a bipartite graph: A bipartite graph G is a simple graph whose vertex set can be partitioned into two mutually disjoint nonempty subsets V1 and V2 such that vertices in V1 may be connected to vertices in V2, but no vertices in V1 are...

Working on a physics lab report regarding uniform circular motion, one of the questions asks to graph the Tension Force vs. the square of the speed. Another part of the same question asks what the slope of the graph represents, which is where I'm stuck.

Homework Statement The figure below shows the acceleration-versus-time graph for a motorcyclist riding along the x-axis. Assume that at t = 0, x = -1 m and v = 2 m/s. Unless otherwise specified, use the graphical analysis to solve all the questions below. Do not use the kinematic equations...

I'm working on simple game and am working on a leveling system, using a function to get experience needed. I am using area under a function above y=0. The first problem, I can't figure out a simple number. f(x) = x2/5 dx Then, looking for area, I'm unsure about a really simple thing. Getting...

Homework Statement How do you find wavelength given this wave graph? [ignore my title please]Homework Equations c= (wavelength)(frequency)The Attempt at a Solution I always see displacement (y) vs distance (x) graph, but this one is displacement (x) vs t I'm kinda confused how you solve...

Bar Pendulum Graph name? Hi! WWhen i did the Bar graph experiment, i obtained a parabolic curve on negative and positive x axes (time period^2 vs distance from cg graph). Can anyone tell me what it's actually called, the actual name of the graph?

Hi! Let the function be f(x,y)=x^2-2*y^2,which graph is S:z=f(x,y).Which are the contour curves?Are these hyperbolas? :confused: Thanks in advance!:)

I am currently taking a combinatorics class that surveys a little bit of graph theory and it piqued my interest. Does anyone have a recommendation for a good introductory book on the subject? I am really interested in finding a book that is very readable and not the standard definition, lemma...

Homework Statement A person falls on a mattress from 4 meters. The mattress does not make him bounce. Draw the speed-time graph. Homework Equations Speed-time graph principles. The Attempt at a Solution I know the first part is a linear function, where the speed increases, because...

For the slope, I got 0.4532 and for B, I got 74.09, but they're both wrong! And my excel program keeps crashing everytime i try to print screen it! This is really urgent and I don't know who else to turn to because this is due very very soon and I'm desperate! Also, what about this one:

Here is the question: http://i259.photobucket.com/albums/hh299/the-real-guitar-hero/Capture_zpsf2b9cd28.png part A = 3√5 b=y=2X+1 c=(0,1) D is where I am confused. Area of triangle = (base x height)/2 from working out, line 2 cuts the x-axis at -1/2. line 1 cuts the x at 7. the height is 3...

Homework Statement Hello all! Basically, my professor used this graph in our lecture, but I do not really understand how to read it. The graph has three variables, so I'm guessing it is Voltage vs. Current as time increases? One question he asked was "The figure shows the voltage and...

I have just finished a unit on constructing taylor and maclaurin polynomials and series. However I am really lost on how to find the answer to this problem that i found online for the test review and its going to be on my test, I know how to construct a maclaurin polynomial and have a vague...

The resistance,R, of a thermistor varies with absolute temperature according to the following equation: R= R0 ek/T I was asked to find the constant k using the graph. I put the equation given in the form ln R= k/t + lnR0 k would be the gradient. So I found the gradient from...

Homework Statement Without a graph, test the suggestion that the speed, c, of the water wave is related to water depth, d, by: c ∝ d^1/2 No other data is given, this is suppose to be collected by myself but I am revising for a practical exam paper without having the data given. Markscheme...

Homework Statement The Attempt at a Solution Netforce is zero right? Constant speed is constant velocity. I'm not sure how to draw this.

Homework Statement Homework Equations a = Δv/Δt v = Δx/Δt x = area under velocity graph The Attempt at a Solution According to my second attempt, the answer to "particle's speed at t = 20.0 s?" is not 15m/s either. Working out picture. I don't understand where I went wrong. I've always...

What I am trying to do right now is graph momentum as a linear slope on a graph. What I know is: p = mv Now, I've collected data giving me the velocity of the object, and I also have the mass. Now All I am trying to do is figure out a way to graph this. I've tried 1/p= 1/(mv) but of...

Suppose we have a group with presentation G = <A|R> i.e G is the quotient of the free group F(A) on A by the normal closure <<A>> of some subset A of F(A). Is it true that that fundamental group of the Cayley graph of G (with respect to the generating set A) will be isomorphic to the subgroup...

You are given a table and (maybe) a picture of a graph. Here are the points given: 0,0; 1,-.7568; 2,.99061; and 3,-.988. What is the function? Is it possible to figure out by hand?

Problem: Which of the wave functions shown might conceivably have physical significance? Solution: I have attached a drawing of the two wave functions. According to my book, the one on the right could have physical significance, while the one on the left does not. Can anyone explain why not...

Homework Statement [PLAIN]http://postimage.org/image/bd4pyoqkt/ Make a sketch of Vout vs Vin for Vin from 0 to 5 V, assuming that both diodes have a diode drop of 0.5 V Homework Equations None that I know of. The Attempt at a Solution The way I see it, the Vout will start at...

I don't understand what this lab I'm supposed come up with will involve. There's going to be a sound generator producing sound waves. We will have a meter stick and a sensor to measure the sound intensity(W/square meters) and sound level(decibels). We will measure the intensity and level at 6...

how do you graph an integral? (a) Evaluate g(x) for x = 0, 4, 8, 12, 16, 20, and 24.(b) Estimate g(28). (Use the midpoint to get the most precise estimate. since there's no equation give I don't know how to integrate the function.

I'm trying to understand the tree-graph on the right side of http://en.wikipedia.org/wiki/Arachnid#Systematics. If I understand well, Opiliones evolved from scorpions, ambyplygi evolved from spiders and schizomida evolved from ambyplygi. Is this right? How do they determine which order evolved...

Hey guys, I'm new to these forums so I am unsure if this is the right place to be posting this, but here it goes. I have been working on a drag spread sheet using OpenOffice Calc to predict where a potato will land when fired from a potato gun. I have gotten pretty far along, using...

Hi all.. another Trig question here... Let's say I'm given a graph of a sinusoidal function and asked to find its equation, but I'm not told whether this is a sine or cosine function and I'm left to determine that myself. I understand that evaluating where the graph intersects the y-axis is...

Homework Statement Hey guys, I have this question. Given a tree T = (V , F), find an algorithm which finds u in V, so in the graph T = (V \ {u} , F) the size of each connected component is |V| / 2 at most. What is the complexity? Homework Equations The Attempt at a Solution...

how can I draw y = arcsec(e^x) where x > 0 and 0 < y < pi/2 I've found the derivative which I got to be \frac{1}{\sqrt{e^{2x} -1 }} however, the graph doesn't seem to have any minimum or maximum points. I don't really know how to test this about, as I don't know what arcsec(e^x) is...

Hello, Homework Statement A gearbox and flywheel are as shown in FIGURE 4. The output shaft rotates in the opposite direction to the input shaft at 5 times its speed. The gearbox has an efficiency of 92%. If the flywheel is solid, has a mass of 50 kg, a diameter of 1.5 m and is to...

I know how to do it but how come after I translate a velocity time graph to a position time graph then reverse it to see if my answer is correct. It doesn't look like the original? Like I am given a Position time graph. I translated it to Velocity. Then I try to translate back to position but...

I can't provide all the information, because I'm on my mobile phone. Here is a shot of the problem: The tangent of each curve is the slope, right? So how do we use that to find vf (instantaneous velocity) at 4s and 8s