What is Graph: Definition and 1000 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. P

    About critical damping resistance of a ballistic galvanometer

    At critical condition, ##\omega=0## so time period will be infinite and so will be ##\lambda##.Therefore, the critical resistance will be the corresponding resistance(plus galvanometer resistance)of the asymptote of ##\lambda## vs. ##R_2## graph(the graph is a rectangular hyperbola). But here's...
  2. Sneaky6666

    I Find Smallest Subtree of G w/ Nodes from S

    I have a unique problem and looking for a known fast algorithm for it. I have an unweighted but directed graph `G`. I then have a subset collection of nodes `S` existing in `G`. I want to find the minimum sub tree in `G` such that it contains all the nodes in `S`. I so far found Chu-Liu/Edmonds...
  3. M

    Analyse motion of an oscillator: x(t)=0.2cos(12*pi*t)

    Hello. I have tried to solve it using x-t Graph. We know that period of this function is ##T=\frac {1}{6}s##. Then I've used ##x(t)=0## to find the times in which the oscillator is at ##x=0##: ##t=\frac {k}{12} + \frac {1}{24}## for ## k \in Z.## Now I can draw x-t graph. We should check time...
  4. S

    Radii of stacked circles inside the graph of y = |x|^1.5

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  5. Sh4dman

    Velocity-time graph from distance-time table

    Question: Answer:
  6. C

    Graph of f' using graphical methods

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  7. K

    Calculating electric charge from graph (capacitor)

    Apparently, we need to integrate the functions from 0 to the time when it is fully charged. However, I integrated in terms of t so the soultion (according to a graph programme) should be around 236 Vs but I don’t see how this could help me.
  8. L

    Combination of 2 formulas for a graph

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  9. Darmstadtium

    I Relationship between the Different Frequency vs Decibel Graph Peaks

    In the popular answer for the coin-mass question of Physics Stack Exchange, I am wondering what are the correlation between the first red peak at around 9kHz and the second red peak at 16kHz. I first thought that they are consecutive harmonics but there was no way of proving it as I do not know...
  10. C

    Points of inflection on acceleration graph

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  11. C

    Graph for sinusoidal wave travelling to the left

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  12. C

    Discontinuous voltage graph for bullet going through metal coils

    For this problem, The solution is, However, dose anybody please know why the graphs for ##V_1## and ##V_2## are discontinuous where they cross the time axis? Many thanks!
  13. C

    Drawing the Graph: Analyzing Solutions and Questions

    For this problem, , The solutions is, However, why did they not draw vertical lines for the graph like this: ? Thank you!
  14. C

    Formula for Xo and Yo for graph of quadratic function

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  15. N

    I Triple equation for integral on a graph

    Hi, so I'm trying to find the volume of a shape using integral, I found the equation of one plane in 3D space but the second one is something like that, which I cannot write in integral as a function: ##\frac{2(2x-a)}{a}=-\frac{2(6y-a\sqrt3)}{a\sqrt3}=\frac{2z-a\sqrt3}{a\sqrt3}## In the 3D...
  16. iceninja3

    Finding acceleration from Velocity vs Position graph

    The answer is E. I was initially very confused as to why the answer was not A but realized that the graph was velocity vs position (rather than velocity vs time) which means I can't simply take the derivative of the given graph. One thing I tried was writing out the equation first(c being a...
  17. Leo Liu

    Analyzing the Effects of Battery Position on ##C_m-\alpha## Graph

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  18. chwala

    Estimating the Gradient of a Graph: Student's Attempt

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  19. Y

    Functional representation of the oscillating graph

    Hi; This is in fact not a homework question, but it rather comes out of personal curiosity. If you look at the graph of the two functions in the image attached, what is the simplest functional representation for such a symmetrical pattern?
  20. H

    A What does Rovelli mean with "oriented and ordered graph"?

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  21. P

    Thermal Energy Graph Question

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  22. K

    What does the 'power' vs 'time' graph look like for a 3 phase AC supply?

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  23. A

    B What Math Class Teaches us how to Draw a Graph?

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  24. knapklara

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  25. Eobardrush

    Velocity-Time Graph problem

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  26. Y

    Graphical Impulse calculation from the graph of force verus time

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  27. mcastillo356

    B Why is Big-O about how rapidly the Taylor graph approaches that of f(x)?

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  28. Alexanddros81

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

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    • Alexanddros81
    • Thread
    • Calculus Graph Software Vector Vector calculus
    • Replies: 2
    • Forum: Calculus
  29. M

    B Why is Delta y not equal to dy for infinitesimally dx on the graph?

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  30. chwala

    Find the set of possible values of ##a## - Modulus Graph

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  31. 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?
  32. M

    How to calculate distance traveled if you know a(v) graph equation?

    I know that you can find the distance traveled by integrating v(t), but I can't find a way to convert a(v) into it. I tried derivating and integrating the a(v) equation, but I don't know what the results mean.
  33. S

    Series bandpass filter graph

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  34. neilparker62

    B Just for fun: Cubic Graph Plot

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  35. F

    Comp Sci Creating a City Graph with Nodes & Edges

    Edit: Trying to fix the formatting... class Node(object): def __init__(self, name): self.name = str(name) def get_name(self): return self.name def __str__(self): return self.name class Edge(object): def __init__(self, src, dest): self.src =...
  36. 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 :)
  37. 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
  38. dark_nebula

    Question regarding a decay spectrum graph

    I am not sure what is the description of Channel.
  39. M

    Spectral Graph Clustering: where does the 'scoring' function come from

    Hi, I was reading through some slides about graph clustering. In the slides was a very short discussion about 'eigenvectors and segmentation'. I don't quite understand where one of the formulae comes from. Context: We have some undirected graph with an affinity matrix (i.e. weighted adjacency...
  40. robphy

    Insights Introducing Relativity on Rotated Graph Paper: A Graphical Motivation

    Continue reading...
  41. karush

    MHB 7.t.27 write eq for a sinusiol graph

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  42. Borg

    Python Understanding Graph Neural Networks (GNNs) Tutorials & Examples

    I've been reading various articles on Graph Neural Networks (GNNs) for the last month or so. In particular, I have been focusing on the tutorials in A Blitz Introduction to DGL. I made it through all of the tutorials OK but I'm having trouble understanding certain aspects of GNNs. I'm also...
  43. 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...
  44. bluesteels

    PV Graph Question: Internal Energy Not Zero?

    Figure 1: im so confused on why is the internal energy not zero for the 2nd picture because i thought if the gas returning to its original states so it zero
  45. karush

    MHB Usaf graph y=sin (x) -2

    Graph $y=\sin{x}-2$ on the domain $[0,2\pi]$ This is a sample math problem in preparation for the entrance exam for the USAF Academy Even not asked I thot also the Period, Amplitude, PS and list some observations that should be know to graph without an app 1. we know that sin(0)=0 so sin(x)...
  46. rudransh verma

    Graph question for 1D motion

    ##v=\frac12 *1*4+\frac12*1*4= 4 m/s## but the answer is wrong.
  47. rudransh verma

    V-t graph problem

    3) and 4) is easy. Average and instantaneous acceleration is same from 1 to 4 sec since it’s constant acceleration. 1) and 2) I am unable to get the correct area under the curve. ##s = \frac 12*(-5)*1 + \frac12*10*2 + 10*1 + \frac12*10*1## Same I guess will be distance. 5) what is the graph...
  48. Andrea Vironda

    Is there something happening below 0°C in this daily temperature graph?

    Hi, I notice from the graph that every night when the temperature reaches -2/-3 °C the curve change first the slope and then the concavity. Is something special happening?
  49. DaveC426913

    B Periodic spiral graph interpretation

    Could someone explain the geometry of this graph? Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021 Why are there two areas - one above and one below - the centre line...
  50. 0

    Moving the graph to the right -- What do you think?

    I'm studying calculus alone with textbooks. The part about moving the graphs to the right or to the left struck me because they just have a list of rules, properties and make you relate the graph with the corresponding equation. I know what is the rate of change and I thought I could do better...
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