# Graph Definition and 101 Discussions

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.

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1. ### I I want to know which software was used to create vector calculus graph

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
2. ### B What is this part of a graph on the axis called?

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?
3. ### Determining the Yield strength and Ultimate tensile strength of HDPE

Help would very appreciated. Also I am new to this website so if something seems wrong please tell me :)
4. ### Making a Velocity vs Time graph for a bullet

Here is my working in case it helps :)Ignore the v = 0.6/0.0001 = 6000m/s
5. ### Plotting the graph of Friction Force vs. time (Laws of motion)

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...
6. ### Plotting wave function

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)...

36. ### How to linearize this data?

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...
37. S

### Calculate the time at which the object changes direction

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...
38. ### A Graph homeomorphic to Sphere

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...
39. ### Graphs of Polar Equations

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...
40. ### Why does not this Erdos-Renyi C code work?

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...
41. ### Graphs of sin and cos, how to set points for x values

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...
42. ### B Do all the peaks and valleys of f have f'=0

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...
43. ### Motion graphs and their units

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...
44. ### I I think I solved divisions by zero

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...
45. ### How stretching a rubber band, affects the range of a shot?

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...
46. ### How the launch angle affects the horizontal distance/range?

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...
47. ### How should I represent a financial market as a graph?

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...
48. ### Show plane curve can be described with graph @ tangent point

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...
49. ### Help Please -- E/M conceptual question regarding electric potential

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?
50. ### I Graphs of sin2x

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...