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.
Hi.
I have the Marsden an Tromba vector calculus book 6th edition.
I was wondering which software was used to create the books graphs.
I attach two graphs as an example.
Thanks
On this graph on the Y-axis just above the origin is a "zigzag" mark (highlighted with the red circle) which represents a discontinuity as the value of Y jumps from 0 to 130. Does this mark have a formal name?
F.B.D Of first block
(I have shown only the horizontal Forces)
f1(max) = μ (1kg)(g) = 0.5 * 10 = 5N
F.B.D Of the second Block
f2(max) = μ (3kg)(g) = 15N
Now the string will become taut and the tension will start acting when f = t = 5N
But for 0<f<5N there will be no motion between the 1 kg...
Summary:: We are currently studying basics of quantum mechanics. I'm getting the theory part but it's hard to visualise everything and understand. We are given this question to plot the function so if someone could help me in this.
Plot the following function and the corresponding g²(x)
g(x)...
Background Information (Not Strictly Necessary):
As a quick recap, the graph I am dealing with is a semi-logarithmic graph of free induction decay (FID) amplitude as a function of time. To acquire the value for ##{T_2}^*## (and its uncertainty) in the graph, I used the below equation to do so...
The 4-colour theorem states that the maximum number of colours required to paint a map is 4.
The proof requires exhaustive computation with a help of a computer.
But I thought that one can visually prove the theorem in the following way;
If one replaces the map with a graph where each region...
Hi everyone!
We launched Connected Papers 7 months ago, with the goal to help researchers visually find and explore academic papers.
Input: a paper of your liking.
Output: a full interactive graph of similar papers to explore.
For example, here is the graph for The Coevolution of Galaxies and...
Hi. I have graph which I am analyzing in MATLAB. I would like to determine sections of the graph which could be removed from the rest of the graph by removing only 2 edges. (The graph represents the network of atomic bonds from a simulation of silica, and I am attempting to locate strands of...
Given the equation : ##|y| x = x##.
Two conditions are possible :
(1) ##\underline{y\geq 0}## : ##xy = x\Rightarrow \boxed{y = 1}\; (x \neq 0)##. We note that except for zero, ##-\infty<x<+\infty## for this case.
(2) ##\underline{y < 0}## : ##-xy = x\Rightarrow \boxed{y = -1}\; (x \neq 0)##...
Hey guys, I need a little help with this exercise so I know I'm on the right path.
My explanation:
The Bellman-Ford-Moore algorithm computes shortest paths in O(nm) time, so in this situation we say that in a directed bipartite graph the number of iterations that the algorithm will do is...
Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions.
This is a GIF of the motion...
Hello, good morning.
I would like to know if someone knows a program to be able to draw the functions in the same way as the one shown in the image and also allow me to point out an enclosure formed by them without having to use inequalities to do so.
Thank you very much for everything beforehand.
When viewing an HR diagram, the main sequence curve is apparent, and the general shape of it is obvious. However, in this truncated version, it's unclear to me exactly which stars should be considered main sequence. I've added a shaded grey area as what I think I should count as main sequence...
I have two questions
(1) If we have two areas, for example one in America and the other on Asia, both with the same latitude φ, which one of the areas will receive more Solar Radiation? Or will it be the same?
(2) If Earth's eccentricity graph for the past 750k years is this...
Homework Statement
Serway Physics Section 2.4 Acceleration
(a) Use the data in Problem 5 to construct a smooth graph of position
versus time. (b) By constructing tangents to the x(t) curve, find the instantaneous
velocity of the car at several instants. (c) Plot the instantaneous velocity...
Homework Statement
Serway Physics Section 2.4 Acceleration
17. Figure P2.17 shows a graph of ##v_x## versus t for the motion of a
motorcyclist as he starts from rest and moves along the road in a straight
line. (a) Find the average acceleration for the time interval t = 0 to t = 6.00 s.
(b)...
Homework Statement
The figure below shows the speed of a person's body as he does a chin-up. Assume the motion is vertical and the mass of the person's body is 72.7 kg. Determine the force exerted by the chin-up bar on his body at the following times.
My answers:
Homework Equations
F = ma...
Homework Statement
Graph the ellipse 4x² + 2y² = 1
Homework Equations
4x² + 2y² = 1
The Attempt at a Solution
2x² + y²/2 = 1/2
I searched for exercises on Google, and i didn't find an equation like that. I watched videoleassons too but it didn't teach this type of equation.
Homework Statement
We're supposed to convert a position-time graph to a velocity-time graph to an acceleration time graph.
These are the values for the position-time graph:
Homework Equations
m = y2-y1/x2-x1
The Attempt at a Solution
I found the slopes for each time which were 5, 8.5, 17...
Problem goes: A rubber ball, travelling in a horizontal direction, strikes a vertical wall. It rebounds at right angles to the wall. The graph below illustrates the variation of the ball’s momentum p with time t when the ball is in contact with the wall.
Which of the following statements is...
Homework Statement
Suppose this the velocity time graph given and we want to plot position time grah from this.
What are the things to be considered while plotting the position time graph from this graph?
2. Homework Equations
The uniform acceleration motion equations.
The Attempt at a...
I have to construct suitable circuits to show the operational principles of some sensors: pH meter, sound, light and temperature. Would these count as circuits? or diagrams? (I'd say diagrams).
I am finding it hard to find circuits showing how sound sensors and pH sensors work etc and the ones...
Hi guys,
Sorry if this has been covered before but I have been searching the forum looking for the exact information and have been unable to find it. I am currently carrying out a project to make a Honda GX35 engine suitable for competing in the Shell Eco-Marathon where I will perform...
Homework Statement
Homework Equations
The Attempt at a Solution
## \sinh (x) ## is continuous.
## \sin{( \sinh (x))} ## should have the same amplitude. .....(1)
Option (a) and (b) follow this condition.
For x = 0, ## \sin ({ \sinh (x)} ) ## = 0. .....(2)
Option (a )...
Homework Statement
Could somebody link me to a youtube video explaining this topic, its from an exam paper at me college and I cant find notes on it.It think it has something to do with limits. Many thanks.
Homework Statement
So I have to make three charts for the measurments that we made in class (physics experiments but it's not important). The first one had to be with a linear trendline, the second one with a exponential and the third one with a logarithmic trendline. For some reason the last...
Homework Statement
[/B]
Sketch in a third vector, C, whose magnitude and direction are such that A+B+C=0. Vectors A and B both have a magnitude of 5 and form a 30 degree angle (image attached).
Homework Equations
[/B]
How do I go about this question? I have no idea how to start or what to...
Homework Statement
Homework Equations
## V=IR##
The Attempt at a Solution
This is an I-V graph so the slope must represent ##\frac{1}{R} ##
Now,
$$ R∝Temperature$$ {This is assuming that the wires are of metal}
Now , since the graph is of ##\frac{1}{R} ## , the steeper the slope the higher...
Hi,
I'm supposed to linearize this set of data:
"Below is a data set which includes information about the motion of the objects in the solar system. Note: the periods are listed in Earth years (time it takes the Earth to complete one orbit around the Sun) and the average distances are reported...
Homework Statement
An object starts from rest and uniformly acquires a velocity of 20.0 m/s in 5.0 minutes. For the next 10. minutes the object moves with a constant speed. After 10. minutes moving at 20. m/s the object then again accelerates and reaches a speed of 15 m/s in the opposite...
Hello,
I want to prove that a graph represent a manifold, for this i take the opposites edges of a vertex (edge connected between vertex connected to the current vertex) and this subgraph need to be homeomorphic for example to the 1-sphere if i want a 2 manifold. This criterion ensure that my...
Homework Statement
Hello!
I will be grateful for your help in deciphering the meaning of a paragraph from the book. I honestly don't understand how they got the semi-circle on the xy graph by transferring it from rθ graph.
Homework Equations
I attach the screen shot from the book.
The...
Homework Statement
I need to write an Erdos-Renyi random graph, by using the adjacency matrix (or alternatively list) and calculate the fitness of the graph.
Definition: G(n, p) is a random graph with n vertices where each possible edge has probability p of existing.
Homework Equations
The...
Homework Statement
Hello!
I am at the topic on graphing trigonometric functions. Exercises are rather easy at this point, but I have a problem deciphering how authors of the book choose points for x values. Please, take a look at few examples (including screen shots I attach), and, please...
I learned in the earlier chapters that peaks and valleys of a fxn have points where f'=0 (i marked them with red x). A few chapters later it said if a fxn has 2 roots, then f'=0 (still the 1st graph).
So does that mean if the graph of a fxn is like the 2nd graph, the peaks and valleys are not...
Homework Statement
I'm having some issues with the following exercise:
The graph below represents the marking of a vehicle speedometer in funtion of time. Elaborate the corresponding graphs of acceleration and space traveled in function of time. What is the average acceleration of the vehicle...
First of all, I didn't know where to put this in general math or differential equations.
Let's start with the basic, x/0 = α. Where α is every number and decimal number from -∞ to +∞, by rearranging, we get x = 0α, x= 0, therefore only 0/0 = α. Now, we can integrate this with graphs.
Take the...
Homework Statement
I did an experiment on how stretching a rubber band, affects the range or distance of a projectile shot.
Variable list:
Independent Variable
Amount of stretching
Dependent Variable
Range or distance
I created my catapults on my own and used two different rubbers bands...
Homework Statement
I'm doing a lab report about how the launch angle affects the range of a projectile.
Independent Variable
Angle of Launch
Dependent Variable
Range or distance
I did an experiment with three trials and here are my results:
And then plotted the data. However, it's a...
Hi guys.
I am reading several papers about financial market and authors show the possibility to represent this market as a graph in which nodes correspond to traders and edges represent trading relationships.
Which programming software could be a powerful tool to write a such code?
I am...
Homework Statement
Provide a complete proof that a regular plane curve γ : I → R2 can near each point γ(t0) be written as a graph over the tangent line: more precisely, there exists a smooth real valued map x → f(x) for small x with f(0) = 0 so that x → xT(t0) + f(x)JT(t0) parametrizes γ near...
So in a graph where V is a function of x, when the slope is negative what does that mean about the direction of the field along the x axis? What about when the slope is positive?
If we look at the graph of sin2x, well its Time Period is pi, and amplitude is same as that of sinx. But if we expand sin2x as 2sinxcosx, rewriting it as 2cosxsinx. According to the Physics in SHM, Wave Motion, whatever is infront of sinx is called as Amplitude. Now, y = 2cosxsinx = Asinx, then...