What is Graphs: Definition and 654 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. B

    Scalings and translations in graphs

    Homework Statement Explain how the parabola that is the graph of f can be obtained from the graph of y=x2 Homework Equations f(x)=-1/3(x-2)2+3 The Attempt at a Solution a y-scaling with factor -1/3 a horizontal translation by 2 units to the right a vertical translation by 3...
  2. W

    Graphs to find minimum days for meetings

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  3. K

    Understanding Derivatives: Function Relationships and Graph Interpretation

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  4. J

    Force graphs and stress-strain graphs

    I know what a force-extension graph looks like. DOes a force-compression graph look the same just with different axis? (compression on the x-axis NOT extension) DOes a compressive-strain graph (Young Modulus) look the same as a tensile stress-strain graph? if not what do they look like...
  5. H

    Help with Graphs: Understanding v(t), v(x) and v(a)

    hey, I am not too great at physics, and i know this is going to seem like a relatively elementary question. when in class we learned about graphs, i never fully grasped the concepts of v(t), v(x), and v(a) graphs, such as how they all correlate to each other, and forming them. I am worried that...
  6. F

    Limit of H(x) for between graphs

    Homework Statement if the graph pf y=h(x) always lies between the graphs of y=x^3 and Y=x^1/3 for what real numbers a can you determine the value of limH(x)x->a? explain and find the limit for each of these values of a Homework Equations The Attempt at a Solutioni can draw two...
  7. O

    Can a graph with no triangles have more than (n^2)/4 edges?

    [b]1. Prove that a graph with n vertices that has no triangles has at most (n^2)/4 edges. [b]2. [b]3. Um so i was thinking maybe you start off with a complete graph and then keep deleting edges so as to remove the triangles within it or something? Or maybe by induction?
  8. A

    Compare graphs of a^x and x^a - pretty simple,

    Homework Statement Compare the functions \; f(x)=x^{7} \; and \; g(x) = 7^{x} \; by graphing both functions. A) find all points of intersection (there is suppose to be 2) B) Which graph grows larger I need help with A Homework Equations The Attempt at a Solution...
  9. M

    Understanding Trajectory Graphs

    Trajectory Graphs?? Homework Statement The trouble I'm having is with determining what information I can get from a trajectory graph and how that information differs from what I can find on a position vs. time graph. Is the acceleration I find just the rate of change in the direction of...
  10. M

    Trajectory Graphs: Direction of Velocity & Acceleration

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  11. G

    LaTeX Plot some graphs to use in LaTeX

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  12. C

    Do Lab Report Graphs Need to Include the Origin Point?

    Homework Statement I have to do a lab report on centripetal force, frequency and radius. My question is, does a graph have to show the (0,0) points? Also, I got an equation out of the graphing software for one of the graphs and it was y = 1.51x^0.4233, is it okay to use this equation or y =...
  13. B

    Projectile Motion Graphs and Velocity Vector Calculation Homework

    Homework Statement In each case, draw a set of graphs for the vertical and horizontal components of motion. Also draw a motion map of the vertical and horizontal components of motion. A projectile is launched with a speed of 30 m/s at an angle of 30 degrees. At a point which is ½ the way down...
  14. J

    Straight Line on Distance vs Time^2 Graphs

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  15. P

    Graph Isomorphisms: Understanding the Concept and Breaking Down Examples

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  16. H

    Minimum veritcal distance between two graphs.

    Homework Statement Calculate the minimum vertical distance between the cubic y=x^3-x^2-4x+4 and the parabola y=-2x^2+16x-30, when x is positive. Homework Equations y=x^3-x^2-4x+4 y=-2x^2+16x-30 The Attempt at a Solution I have no idea at all how to work this out, so perhaps someone...
  17. B

    MATLAB Acquiring images and plotting graphs using Matlab

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  18. S

    Plot some 2d graphs in a 3d fashion

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  19. tom.stoer

    Graphs, embeddings and dimensions

    Hello, Let's start with a cellular decomposition of 3-space, a "foam". A foam can be represented by its dual graph: cells and faces are dual to vertices and links. What about the opposite? It is clear that one can construct graphs for which no dual foam exists: take a large foam and...
  20. T

    C/C++ Creating Graphs in C++: A Beginner's Guide

    Hi, I have just started to learn C++ after a year programming with IDL. I realize this is probably a really stupid thing to be asking but what syntax should I use to display my data. To start off with I just want to plot a simple x-y graph. I have my arrays all ready, what do I type? Can C++...
  21. T

    Finding Solutions to 4x + 60/x = 40 by Drawing a Suitable Line

    Homework Statement Draw the graph of y = 3x + 60/x - 35. Range : x= 1.5 less than or equal to 10 y= 9.5 to 1 Find Gradient **Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line. Homework Equations none The Attempt at a Solution The graph is...
  22. K

    Local min/max/saddle points of 3d graphs

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  23. B

    Help creating graphs, number lines, etc and formatting them into a larger document

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  24. N

    What Is the Best Graph to Represent Mode, Median, Mean, and Standard Deviation?

    Homework Statement So i have collected the following data and it now asks me to present the information in an appropriate graphical form but I am not sure how. mode – = 29 liters Median – = 36 Mean – = 35.13 Range – = 17 Standard deviation = 4.87 Interquartile range = Q3 – Q1...
  25. N

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  26. R

    MATLAB Help Smoothing MATLAB 3D Graphs

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  27. T

    Help with simplifying derivatives when sketching graphs

    Homework Statement Sketch the graph of x ^ (4/9) * e ^ (-x) Homework Equations None. The Attempt at a Solution My y' = -x ^ (4/9) * e ^ (-x) ( 1 - 4/9x ^ 1/9). I keep on getting a reaaally long derivative for y'' and thus cannot place it on my sign table. Could someone please...
  28. L

    What value of x do the graphs of f and g have parallel tangent lines?

    Homework Statement Let f be the function given by f(x) = 3e^2x and let g be the function given by g(x) = 6x^3. At what value of x do the graphs of f and g have parallel tangent lines? a. -0.701 b. -0.567 c. -0.391 d. -0.302 e. -0.258 Correct answer is c. -0.391 Homework...
  29. A

    Can the number of edges determine isomorphism in graphs?

    Hi all, If I have to prove that the graph G and its complement G' are isomorphic, then is it enough to prove that both G and G' will have the same number of edges. Intuitively its clear to me, but how do I prove this. If there's a counterexample, please post. Thanks in advance.
  30. T

    Plot the graphs of power dissipated in pure resistor

    I am trying to plot the graphs of power dissipated in pure resistor , pure capacitor and pure inductor against time . My question is when i plot the voltage and current graph for pure resistor , i know they are in the same phase , but V0 is greater or Io is greater , i think Vo is greater...
  31. P

    How to find integrated peaks on NMR graphs

    Hi all, I am currently self studying a chapter on Modern Analytical Chemistry. One part talks about interpreting NMR graphs and I understand the basic gist of it, however, I don't understand how to find the integrated peaks. I've looked extensively online and I now understand that you have to...
  32. D

    Symmetry in Graphs: Conditions & Possibilities

    For a graph of any function, one of following conditions is said to exist so as for it to be symmetric: a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists. a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists. a graph is...
  33. S

    A question about constant velocity/constant acceleration graphs?

    Hey! For a lab, I have to make a few graphs, I just need some clarification. Please correct me if I'm wrong. For a D-T graph, where velocity is constant, the line will be straight. (Diagonal.) For a V-T graph, where velocity is constant, the line will be straight. (Horizontal) ^ Confused...
  34. G

    Graph Theory and Bipartite graphs

    I have a problem involving graph theory. This is not a graph theory course though so I do not know much about it. If we have complete bipartite graphs consider whethere or not they are graceful. A graph is graceful provided the vertices of the graph can be assigned v distinct integers...
  35. S

    Deriving the Decay Rate Function from Mass & Time Graphs

    Hi. We are given a table containing values of mass(m) and time(t). We have been asked to plot graphs of (m) against (t) and then log(m) against (t). The question is: FROM YOUR GRAPHS, DETERMINE THE FUNCTION FOR THE RATE OF DECAY. Of course i know the formula but have no clue how to...
  36. I

    What Do Velocity-Time and Acceleration-Time Graphs Look Like in Circular Motion?

    Hi guys, I am very new to the forum (and physics itself). I have only started my O'levels but am a deep physics enthusiast for interesting problems. When you have circular motion, and you take the displacement from a point on the circle, what type of: Velocity-time graph...
  37. Buckethead

    Graphs of galaxy rotation curves?

    Can anyone direct me to a good source of graphs of galaxy rotation curves. I need graphs that show both the observed curve data points and the expected curve along with the names of the galaxies and labeled axis. Thanks
  38. S

    Help with VT graph and DT graphs

    Hi Guys, I messed up bad on a recent quiz on these easy VT and DT graphs. I am having trouble going from one to another. I recently took this quiz and pretty much got everyone wrong since then I have googled and read the chapter as much as possible, but I can't find any good completed examples...
  39. T

    Intercepts and Graphs: Understanding the Use of 'OR' in Sketching Y=(x-2)(x-3)

    Alright let's says for example we were to sketch y=(x-2)(x-3). You would find x intercepts and you would write it as x-2=0 OR x-3=0, thus x=2 OR x=3. Why do we use the word OR when we use both of the intercepts to sketch the graph anyway? Why cannot we use AND instead.
  40. L

    How Do Reaction Forces Change as a Man Walks Across a Beam?

    1. A man of mass 75kg walks along the beam shown in the attached file, of length 5m and mass 100kg, from pivot A to pivot B. Draw graphs showing how the reaction forces FA and FB vary as a function of the man's position. Homework Equations 3.I'm not so sure what should be on the...
  41. S

    Mathematica Mathematica - Plot two 2D graphs with different command in one figure

    Good day to all, 1) I find difficulty on putting two 2D graphs into one figure. If same command it is easy to do but i have different commands, the commands are listlineplot and plot...
  42. A

    Finding areas between graphs

    find the exact area between y=ex, y=2, and the y axis im not looking for a solution, just hints on how to get started. would i just go ahead and integrate the function from 0 to 2 or would i solve the function for x and then integrate or are those 2 idea just completely wrong? thanks
  43. D

    Integrating Graphs with Two Intervals: How to Find the Mean?

    In general, if f(x)=k but only for a < x < b and c < x < d how would you integrate the graph ? To find the mean for example, would you find the mean for each and add together, or is there some special thing for this case?
  44. V

    Maple Generating Graphs with Maple: Calculating F_o, w_o and w

    I find the equation of beat: x(t) = [\frac{2F_o}{m(w_o^2 - w^2)}sin(\frac{(w_o - w)t}{2})]sin(\frac{(w_o + w)t}{2}) What values do I get to F_o, w_o and w to generate the graph ? I use program maple to plot graph.
  45. R

    Question on irreducible versus reducible Feynman graphs

    Consider the functional: (1) \mbox{ }e^{iW[J]} = \int d \hat{\phi} \mbox{ }e^{i\int d^4x \mbox{ } \mathcal L(\hat{\phi})+J\hat{\phi}} Define a Legendre transformation to get a functional in \phi(x) instead of J(x): (2) \mbox{ }\Gamma[\phi]=W[J(\phi)]- \int d^4x \mbox{ } J(\phi) \phi...
  46. A

    Cable theory - calculating cable length using graphs

    Homework Statement Using a simulation program I must determine cable length (lambda), area specific conductance (Gm) and internal resistivity of a cell. The program allows you to inject a current (in uA) and change the electrode distance from the centre of the cell. The simulator...
  47. B

    Plotting Graphs for Physics Labs - Maximize Scale & Break Axis

    So I have a lot of physics labs to write up, and when drawing graphs (using experimental data) I have a tough time 1)Determining the best scale so my graph is as big as possible. 2)Determining the best scale so intercepts(y) appear on my graph. Also, I would like help on "breaking the...
  48. H

    Mathematica Drawing more Complicated Graphs in Mathematica

    I have a function, S[q] which is obtained by integrating another function, A[r,q] over r. My problem is that the lower limit of integration, rmin depends on q in a complicated manner. Mathematica can however solve this equation to give several routes, only one of which is real which is the...
  49. S

    Identifying Parametric Equations from Graphs

    Homework Statement http://img704.imageshack.us/img704/5760/pqg.jpg Homework Equations The Attempt at a Solution So i know that graph 2 is C also i know that A and G can't be any of those because its a circular shape.. the rest i have no idea how to do in order to get those...
  50. Y

    (A puzzle) The largest size cliques in n-grouping graphs

    (I apologize in advance for the abuse of the word "group" in this problem. It does not mean a group in the mathematical sense). Imagine you have n^2 objects that need to be grouped in n groups of size n each. Let's call one such arrangement an "n-grouping." You can create n-groupings in...
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