In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection.
Plane graphs can be encoded by combinatorial maps or rotation systems.
An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called a planar map. Although a plane graph has an external or unbounded face, none of the faces of a planar map has a particular status.
Planar graphs generalize to graphs drawable on a surface of a given genus. In this terminology, planar graphs have genus 0, since the plane (and the sphere) are surfaces of genus 0. See "graph embedding" for other related topics.
Can someone explain to me why |2-x| would have a horizontal translation to the right? When I've always been taught that anytime you see a [+] it will translate to the left. The graph would be a regular |x| graph but it is shift 2 spots to the right. Thanks to anyone for help
Hi! I'm a bit stumped on this computer-science-related statistics (I think that's what it would fall under) problem. It's over here:
http://math.stackexchange.com/questions/796517/correlation-between-the-degree-of-two-vertices-in-an-undirected-graph/796526?noredirect=1#796526
It would be...
Question 4b: http://www.skinners-maths.co.uk/specimen%20A%20level%20papers/EC3paper/EC3sh_H.pdf
I wrote out that (1)(a+b)=1 and (-5)(a+b)=-1 but that doesn't seem to work? I know you can solve it directly by substituting in the co ordinates from the graph, but is there an alternative to doing...
Homework Statement
Find the area of the region.
Interior of: r = 2 - sin(b)
Homework Equations
A = 1/2 ∫ (r)^2 dr The Attempt at a Solution
I really don't have any idea how to approach this problem. I don't understand how to determine my limits of integration. The only part of the problem I...
Homework Statement
Draw a graph of xcos(1/x)2. The attempt at a solution
I've differentiated the equation using the product rule.
This got me to:
cos(1/x) + sin(1/x)/x
What I don't know how to do is actually go about drawing the graph. This is also a past paper question for an exam where I...
Please see question 9ii:
Paper: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20QP/6664_01_que_20120307.pdf
Mark scheme: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20MS/6664_01_msc_20120123.pdf
This is my...
Can someone explain to me the concept of this graph and how it works with relation to y = mx + c ?
Usually the gradient is something simple but this time I have no idea... Also, the c intercept, what is the c intercept? As far as I am concerned it is 1 but what does the fact it is 1 mean...
Hmm I'm having issues with an optional problem for some review for a quiz later tonight.
Determine the Quadratic Function for the Graph
the points labeled are X intercepts =(-3,0) (5,0); Y-Intercept = (0,-30), Local Min/Vertex = (1,-32)
It's the parabola looking problem at the bottom right...
Homework Statement
for this question, i only know that E=-L dI/dt... the ans is C , can anyone explain how to get C?
Homework Equations
The Attempt at a Solution
As part of a Physics experiment I have to investigate how the amplitude of a pendulum bob (attached to a string) varies with the number of oscillations it undergoes. The equation I have to work with is:
(where t = the number of swings, A = amplitude after t swings, A0 = initial...
Homework Statement
The function y(x, t) = Asin(kx−ωt+ϕ) where x is in metres and t in seconds for
(a) tp = 3.5 s and (b) xp = 3.7m
The Attempt at a Solution
I don't even know where to begin.
I know λ = 2pi/k
this is really disorienting. In the first graph, I'm given t = 3.5.
A = 3
y(x,t)...
Homework Statement
A head on collision between mass and mass B occurs as described in the F vs s graph below.
Complete the table in the data section
Find \vec{x}A
Find \vec{x}B
see attached page for clarification
Homework Equations
P=m*v
\DeltaP=F*t
Ek=\stackrel{1}{2}mv2
\vec{d} = \vec{v}t...
Urgent!How to find the point where Maximum Curvature occurs on graph?
Homework Statement
The graph(2D) is plotted from experimental data, not from a given equation and within certain limit. I want to know the x&y coordinate where the maximum curvature occur via software means, not manually...
why do we square the value of T ( time period) while plotting the graph of effect on time period of a pendulum with change in its effective length ?
also while deriving the formula of
T=2∏√(l/g)
why do we take T^2 = 1/g.
Whats the need for squaring the time period ?
Homework Statement
There are n amount of wi-fi networks in a given neighborhood. For every pair that are within 50 yards, the frequency used must be different, otherwise there will be interference. How few frequencies are required so that every wi-fi network can be assigned a frequency without...
Homework Statement
Homework, from Modern Graph Theory by Bela Bollobas, section on extremals:
1. Suppose that G is a graph with n > r + 1 vertices and tr(n) + 1 edges.
(a) Prove that for every p with r + 1 < p <= n there is a subgraph H of G
with |H| = p and e(H) >= tr(p) + 1. [Hint: Try to...
Hello all, I'm a bit stumped when it comes to formal proofs. I
PART A: "Let A,B ⊆{1,2...n} be two sets with A,B > n/2. Prove that the intersection of A ∩ B is nonempty."
This part I used contradiction, but didn't get everything. I assumed that if the intersection of A and B was empty, then A∪B...
Homework Statement
according to my book, there's no graph for F versus I , can someone expalin why? based on my understanding it should be a straight line graph ( directly propotional) since F= BIL SIN TETHA
Homework Equations
The Attempt at a Solution
Plotting a graph of acceleration agains displacement (x)
A mass of 0.3kg suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released calculate:
A) frequency of vibration
B) max velocity
C) max acceleration
D) mass...
I'm really stumped here as usual. Here is what I've managed to figure out.
I'm given two equations.
r=2
r=4cos(theta)I converted them both to rectangular coordinates to get an idea of what the graph would look like.
I need to find either the area in red or the area in green. (In this case...
This isn't exactly homework, for which I am not posting in the homework section. I am currently doing my undergrads, and am in the second semester of my first year. I am going to give my finals which start from tomorrow, with the first subject being Electrical Circuits II. I was solving the past...
So here is the problem I am trying to figure out. This is for an Sociology Independent study, so this isn't a homework assignment, but for the greater good of humanity. ;)
First a few "rules".
-There is Graph A.
-The x-axis is 100 units long, 1 being the left end, 100 being the right.
-It is...
Homework Statement
The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?
The Attempt at a Solution
I'm totally lost with...
Homework Statement
I have been given three velocity-time graphs, and have been asked to use the data from these to create position-time graphs. Each graph represent a route that generally goes south. Changes in direction to go east or west and gradual changes in velocity and time to stop at...
Homework Statement
I had a different problem before about this and I figured it out. I'd like to know if I'm doing this one correctly as well.
Count the number of automorphisms in the graph.
The graph is attached, now.The Attempt at a Solution
I know I can rearrange the (a,m,b) 3! ways. I...
Calculate area D=(x,y): -1≤X≤0 0≤Y≤ X²+4x+5
I started with dA=f(x) dx
∫f(Y=x²+4x+5) [F(x) x^3/3 + 2X²+5X] higer limit 0 lower limit -1
F(0)=0
F(-1)=-3.5
F(a)-F(b) = -3,5
I don't get this ... ??
What am i missing?
Regards!
I have an equation for determining the acceleration of an object being propelled by a constant power source, that is affected by air resistance:
a = \frac{P}{mv}-\frac{CDpAv2}{2m}
Since F = \frac{P}{v}
I am trying to graph this as a velocity-time graph, however, I don't know how to do it...
Homework Statement
The a-s graph given below belongs to a bus traveling along a straight road.Given that the velocity of the bus is 10 m/s when s=0, plot the v-s graph of the bus.
Homework Equations
∫vdv=∫ads or 1/2(v2^2-v1^1)=(area under a-s curve.
The Attempt at a Solution...
I thought I'd just quickly tell you guys why I want to graph this equation before giving it you.
We're studying conic sections at the moment, and I started wondering what would happen if I let the directrix be a parabola. I looked at the instance where the directrix is y=x^2. I let the focus...
A) The graph shows V-I curves for two conductors. One is measured for a carbon resistor and obeys Ohm's law; the other is for a light-emitting diode (LED) and shows non-ohmic behaviour. What is the resistance of the carbon resistor?
B) For what value of current is the resistance of the LED...
I recently wrote a program that implements a slightly modified version of Prim's Algorithm to find a minimal spanning tree and it seems to work correctly. However, I am doubtful because my prof claims that this certain tree has more than 1 solution but my program gives only one solution. Note...
Hi, this is part of an application note entitled "Low-Noise Amplifier Stability Concept to Practical Considerations" from Maxim.
Could you help me with the question in the picture? Thanks.
Source: http://www.maximintegrated.com/app-notes/index.mvp/id/1849...
Homework Statement
Given the graph (see picture), determine:
a) magnitude of impulse (max error of +/- 25%)
b) direction of impulse
c) mass of the object that the impulse acted on.
Note that initial velocity is 3.8 m/s to the west and that final velocity is 4.8 m/s to the east.
Homework...
Homework Statement
Homework Equations
P = dW/dt
Change in work = Change in Kinetic Energy
The Attempt at a Solution
Since the integral of the power graph is work done in the system, and since it starts at 0, does this mean kinetic energy is the same thing? So I can probably make...
1. The problem
For sake of format I attached the a screenshot of the course material I'm having difficulty wrapping my walnut around. Which is how:
Total Displacement = Area of Triangle + Area of Rectangle
or
Δvector d = Atriangle + ARectangle
or
Δvector d = 1/2 (V2-V1)Δt +V1*Δt...
The graph in the picture attached describes the motion of a 500.0 g cart for the first 60 seconds of its motion.
1. Calculate how far the cart moves during the fi rst 25 seconds of motion.
2. Indicate the time intervals during which the cart has a non-zero acceleration.
3. Calculate the...
Hi,
For some reason, when I run this MATLAB code, I'm getting what looks like about 10,000 for Rf for the largest Vo on the graph, but MATLAB is giving me Rf at (Vo)max as 100,001
Any ideas?
clc;
clear;
close all;
syms Rf
Rf = 0:0.1:100000;
VRt25 = 18.*(10000)./(10000 + Rf)...
I recently took a test with a question like the one I have attached above. There were four line graphs (I've only included one) with four solutions (I've only included two). I do not remember the question. I am hoping someone can identify the problem, and point me in the right direction...
Homework Statement
I got a graph with time on the x-axis, and distance on the y-axis. (see attached picture)
I have to calculate the acceleration using only the distance - time graph.
Homework Equations
I used S(t)=S(0) + V(0) * t + .5 * a * t2
The Attempt at a Solution
That...
Homework Statement
For my physics coursework I need to convert a curved graph into a linear graph. This will allow me to calculate the acceleration of the object.
The experiment was repeated multiple times with the independent variable being the mass of the object. The object was dropped...
Homework Statement
I am given the graph of the potential of a particle, and the particle is in its ground state. I must make the graph of the wave-function with respect to x.
(A) Sketch psi(x) for this particle.
(B) You make a measurement to find the particle. Indicate on your graph...
Homework Statement
Is a function that has a square root an exponential graph since you can rewrite a square root as x^1/2?
Homework Equations
The Attempt at a Solution
Homework Statement
The graph of the function f is given, Draw the graph of f'
The graph looks like that of a parabola extending continuously upwards to the left and the right.
Homework Equations
lim f(x+ delta(x)) - f(x)
delta x -> 0...