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. Alexanddros81

    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. I

    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. Anmol Dubey

    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. Anmol Dubey

    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. SpectraPhy09

    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. I

    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)...
  7. N

    Position vs Time graphs

    The graph: 1) $$v_1 = \frac{\Delta{x}}{t} = \frac{5 - 3}{3} = \frac{2}{3}$$ $$2 = \frac{\Delta{x}}{t} = \frac{4 - 0}{5 - 1} = 1$$ $$\frac{v_2}{v_1} = \frac{1}{2/3} = \frac{3}{2} = 1.5$$ 2)Points of intersection of the lines with the x-axis: ##I## (0; 3) and ##II## (0; -1), thus $$\frac{2}{3}t...
  8. Athenian

    Finding the Magnetic Field (B_0) on a Graph [NMR]

    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...
  9. A

    B 4-colours theorem can be proved visually

    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...
  10. Discordy

    Studying Connected Papers: a visual tool to find and explore academic papers

    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...
  11. person123

    MATLAB Computing Sections of a Graph Which Can Be Removed By Removing Two Edges

    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...
  12. brotherbobby

    Which points on the plane satisfy the given equation?

    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)##...
  13. SadPaul

    Comp Sci Shortest path problem in bipartite graph

    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...
  14. Sabertooth

    Expressing Elliptic Orbitals As Speed Functions.

    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...
  15. FireAP

    B How would one plot the space-time continuum graphically?

    How would one plot the space-time continuum graphically(if it were possible,obviously)?
  16. N

    ProProgram for drawing functions

    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.
  17. M

    Pipe frictional loss graph

  18. Drioton

    How do I find the area of the region bounded by following?

    Using integrals, consider the 7 requirements: Any my attempted solution that I have no idea where I am going: And the other one provides the graph:
  19. S

    I Main Sequence Rules

    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...
  20. QuarkDecay

    I Solar Radiation/Eccentricity

    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...
  21. Alexanddros81

    Use the data to construct a graph etc.

    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...
  22. Alexanddros81

    Given a graph find aceleration

    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)...
  23. devilish_wit

    Difficult time with motion graphs & dynamics

    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...
  24. José Ricardo

    Ellipse graphic

    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.
  25. john-b

    Inconsistency in a Velocity-Time Graph

    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...
  26. PhysicsIsKillingMe

    Ball-Wall collision problem

    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...
  27. navneet9431

    Steps for converting one type of graph to the other?

    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...
  28. D

    I What counts as a circuit?

    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...
  29. G

    2 Dimensional Kinematics Help -- Finding Gravitational Acceleration with v initial and a trajectory

    Help with the picture posted!!
  30. A

    Plotting a Power Graph using Torque & RPM

    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...
  31. Pushoam

    Graph of ##\sin(\sinh x)##

    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 )...
  32. M

    Can somebody tell me what this topic is?

    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.
  33. A

    Graphic in excel for practicum

    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...
  34. F

    How to draw this vector

    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...
  35. shihab-kol

    I-V graph of two wires and temperature

    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...
  36. F

    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. kroni

    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. Vital

    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. V

    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. Vital

    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. A

    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. Bunny-chan

    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 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. R

    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. R

    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. V

    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. M

    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. M

    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. Apurv Zoad

    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...
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