What is Graphs: Definition + 654 Threads

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. A How Can I Compare Parton Distribution Functions Without Data from Other Groups?

Hello I plotted the Parton distribution functions in Mathematica. Now I want to compare the graphs drawn with the graphs of other groups(xu and xd). How should I do this?

3. B Kinematic equations ##\textbf{purely}## from graphs

1. The first equation between velocity ##v## and time ##t## can be derived using the graph I have drawn for the purpose as shown on the right. Since acceleration ##a_0## is a constant, the graph of ##v-t## is a straight line. The slope of the line is ##\dfrac{v-v_0}{t} = a_0\Rightarrow \boxed{v...
4. I Questions about these Trigonometry Graphs involving sin() and cos()

Hi. I have two trigonometric equations whose graphs I am trying to understand. Here are the equations: 1. a sin(x) - b cos(y) = y; a = 2, b = 2 2. a sin(x) + b cos(y) = 1; a = 1, b = 1 My question is why the graphs are the way they are. What should I do to understand them? Can anyone...

6. Location of point mass based on graphs

Since figure (a) shows the waveform at t = 1 s, I also look at figure (b) when t = 1 s. The value of y is zero so I try to find the location of x from figure (a) for which y = 0. There are two value of x, 0 and 2 m. Let say x = 0 is point P and x = 2 m is point Q. The period is 4 s so at t = 1...
7. I Two Waves In Phase: Exploring the Possibility w/ Graphs

May I know how is it possible for two waves to be in phase when they have different amplitude? I couldn't find any existing graphs that clearly shows how the two waves are in phase, would anyone be able to sketch it out so I can have a look. Thank you:smile:
8. Solving Distance Traveled Using Formulas vs. Graphs

So basically I wonder why the distance traveled by a body in the 5th second gives different results when calculated by the formula for accelerating body(##d=V_0\times t + \frac{1}{2}\times at^{2}##) and when calculated using a graph(formula for the surface of the triangle). Here is the graph of...
9. Analyzing Motion: Deriving Displacement Graphs from First Principles

Initial displacement is h above the ground ie ##s\left ( t =0\right )=h##. I've chosen the ground as the vertical origin with upwards as the positive direction. Gravity will therefore always act in negative direction throughout. Here are the graphs I which to reproduce from first principles...
10. Checking Graphs: Are the Results Accurate?

I have attempted this question - Are the graphs correct?

12. Find the unknown values in the problem involving trigonometry graphs

This is the question... My attempt on part (i), ##b=\dfrac {16π}{2π}=8## ##11=a sin 32π+c## ##c=11## ##5=-a\frac {\sqrt 3}{2} +11## ##10=-a\sqrt 3+22## ##12=a\sqrt 3## ##a=\dfrac {12}{\sqrt 3}## Is this correct? Thanks...
13. Find the unknown values in the problem involving trigonometry graphs

My interest is on finding the value of ##A## only. From my calculations, ##A=1##and not ##2## as indicated on textbook solution. In my working we have; i.e ##4=A +3.## The values of ##B##and ##C## are correct though. Kindly advise. Find the question and textbook solution.
14. Comp Sci Using Single Source Shortest Path Algorithm to find the longest path

This is the weighted, directed acyclic graph I created in JavaScript class WeightedDirectedGraph { constructor() { this.adjacencyList = {}; } addNode(node) { if(!this.adjacencyList[node]) { this.adjacencyList[node] = []; } } addEdge(node1, node2, direction, weight) {...
15. I {Edit-Solved} Confirmation requested on deriving functions from graphs

So I thought that the graph tries to tell us that the function is periodic after 2π interval. So I tried to derive its function from the graph as follows using the point slope equation form for the points (0,0) & (a,π): ##y= ({a}/{π})*x## I hope this function is alright and I just need to find...
16. I The number of intersection graphs of ##n## convex sets in the plane

Let ##S## be a set of n geometric objects in the plane. The intersection graph of ##S## is a graph on ##n## vertices that correspond to the objects in ##S##. Two vertices are connected by an edge if and only if the corresponding objects intersect. Show that the number of intersection graphs of...
17. Motion in 1D-Graphs: Is Option D Correct?

I think Option C should be correct since the body has two velocities in the same position which is not possible. They even didn't show an arrow that could tell it has which velocity at its starting point and at the ending point But the given and in my textbook is Option d ( It can have an error...
18. Showing existence of an Edge s.t. Graphs T1' , T2' are Trees

Attempt - I am stuck at this problem for hours, couldn't make any progress. Still, here's what I've done : Let ## e_1 \in E_1 \setminus E_2 ## be arbitrary. Suppose for the sake of contradiction that ## \forall ## ## e_2 \in E_2 \setminus E_1 ##, ## T_1' = \langle V,(E_1\setminus \{ e_1 \})...
19. What is the intersection point of two objects on a position vs time graph?

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...
20. Is it possible to make graphs of subsets of Rational Numbers in Mathem

Is it possible to make subsets of rational numbers in Mathematica using the plot command, or any other command? Ie., say I want to graph the set of rational numbers from 0 to 1.
21. Graphs of s, v and a for a mass with a piece of paper attached

I understand that velocity is defined as the rate of change of position or the rate of displacement; and that acceleration is defined as the rate of change of velocity (it is the derivative of velocity). Morever, I believe I know that for SHM these graphs vary sinusoidally (I have attached a...
22. A Question about plabic graphs in the amplituhedron approach

I have a few questions on these graphs. For example if there is a way to tell directly from a complicated graph if it is "physical" in the sense that it describes an actual process. I have also questions on the building of graphs using BCFW bridges, on determining the value of the parameter "k"...
23. Good programs to make graphs (complex systems) in linux

Hi guys, my questions is simple and direct. I'm new in the study of complex systems and would like to know which programs are suggested to use to build a graphs, some thing as 1500 connected points. Thanks a lot!
24. Find the corresponding graphs for the distance-time graphs

now there is something i am not getting here, consider for instance graph ##a##, analyzing this graph i can say as follows; between time ##0≤ t<1, ## the velocity is increasing... at time ##t=1##, also reffered to as being intantaneously at rest, at this point we have acceleration ##a=0##...
25. B What Is the Physical Significance of Logarithmic IV Graphs in Diodes?

Hello there, I've been working through a task (that doesn't have an answer sheet or explanation) in which we plot I against V for three different diodes. Each has a different threshold voltage and displays the usual charcteristic curve. The final question is this: "It is suggested that the...
26. NTC thermistor heat dissapation calculation with graphs

I couldn't solve this problem. Any tips or help would be appreciated. If I am violating against any rules please comment, as this is my second post :-).
27. What is the relationship between velocity and time on this graph?

This is the graph I was given and the answer options. Since the graph is a straight line moving towards the positive direction I thought that meant it was traveling at a constant speed moving in the positive direction. That ended up being the wrong answer. Can anyone offer insight, I missed each...
28. I Proof involving functional graphs and the injective property

Definition: Let ##G## be a graph. ##G## is a functional graph if and only if ##(x_1,y_1) \in G## and ##(x_1,y_2) \in G## implies ##y_1=y_2##. Problem statement, as written: Let ##G## be a functional graph. Prove that ##G## is injective if and only if for arbitrary graphs ##J## and ##H##, ##G...
29. Stress-Strain Graphs of different materials

Hello, so I am not actually seeking help sketching the stress strain graphs. However, I am rather confused about the last part of the question to comprehensively label the stress-strain graph of copper with the limit of proportionality etc. Evaluating the graph, it becomes clear that these...
30. I Proof involving functional graphs and the injective property

My only qualm is that the statement “Let G be a functional graph” never came into play in my proof, although I believe it to be otherwise consistent. Can someone take a look and let me know if I missed something, please? Or is there another reason to include that piece of information?
31. Conundrums on energy and graphs

1. I wanted to clarify if Kinetic energy is always positive. Since KE = 1/2 mv^2, and m and the square of v is positive. I assume as such. 2. Given that I have a scenario where an object which was traveling at a positive velocity in a certain direction (we take this direction as positive)...
32. The Datasaurus Dozen

Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing
33. Lift and drag coefficients vs AoA graphs of a specific NACA profile

Hello, I would like to understand know how the lift coefficient ##C_L## versus AoA curve and the drag coefficient ##C_D## versus AoA curve are determined for the various tabulated NACA profiles. Are computer simulation run for the different profiles assuming a certain Reynolds' number? Or can...
34. MHB Bipartite Graphs: Does $\alpha(G) =|U|$?

Let $G$ be a bipartite graph with bipartition $U$ and $W$ such that $|U|\ge |W|$. Is it true that $\alpha(G) =|U|$?The answer is false, but I don't know how to justify it. I would appreciate any help.
35. Stuck doing parametric natural log graphs

I got stuck when i eliminated the parameter.
36. I Why is this unit used in graphs; keV/amu ?

I see various graphs in papers about atomic collisions in units showing "keV/amu". Why is this unit used, why not just "keV" when, presumably, it is the overall keV of an atomic collision that is important?
37. Position in Velocity-Time Graphs

Would it be correct if I multiplied the time by the velocity of the object since the units would cancel into meters? So for example, I multiply 2 seconds by 1m/s which gives me 2m - would that be the object's position?
38. MHB Linear profit, graphs and equations.

I have no clue how to interpret this problem and where to start to get my values to plot my graphs and get my x, y and etc values as there is too much going on. Can someone shed some light of how to do this problem? I am not sure if is this how I solve this: How do I find that the HD...
39. A How to interpret N(E) vs. E graphs when performing Auger spectroscopy

Hi all, my name's Ethan and I'm an undergraduate physics student conducting research on work functions this summer. I've been trying to understand the graphs of N(E) or N'(E) vs. auger electron energy for several days now, but I can't find in the literature what exactly N(E) or N'(E) are. I've...
40. I  Find Two Equal Length Paths in a Tree Graph

In order to try and sovle this problem, my idea here was to use an extremal argument, with two equal length maximum paths on a tree. I said that no matter where the two graphs started, they'd end up having to cross paths since if there were two distinct paths with equal lengths the graph would...

42. Focal length of converging thin lens graphs

I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p) => M+1= -f/p => -Mp-p=f But since it’s the y intercept, p will equal zero and so the focal length will be 0?
43. I When is it preferable to use semi-log and log-log graphs?

Hello, Given two sets of data, ##x## and ##y##, let's assume that the variable ##y## has a range of values that is much larger (or much smaller) than the range of ##x##. It becomes then preferable to convert the ##y## variable's values to its logarithmic value and obtain a semi-log graph by...
44. Graphs, functions, and coordinates

Homework Statement If a staight ε: y=(-λ+μ)x +2λ -μ , (where μ and λ are real numbers) passes through point A(0,1) and is parallel to an other straight lin. ζ: y= -2x + 2008 find λ and μ Homework EquationsThe Attempt at a Solution It is clear that when x=0 we know that 2λ-μ=1 which is one of...
45. MHB Can Vector Space $(V,O_1,O_2)$ Represent 2 Graphs?

Given a basis of a vector space $(V,O_1,O_2)$ can it represent two different non-isomorphic graphs.Any other inputs kind help. It will improve my knowledge way of my thinking. Another kind help with this question is suppose (V,O_1,O_2) and (V,a_1,a_2) are two different vector spaces on the...
46. LaTeX My Cool Graphs: Explore the Possibilities

Just got interested in cool graphs. Here are some I made: https://www.desmos.com/calculator/19lqdi8yid https://www.desmos.com/calculator/zc6qajdh3d https://www.desmos.com/calculator/zsydsv714y
47. MHB Why Can't Two Functions Cover the Unit Circle?

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 3.1: Manifolds ... I need some help in order to understand Example 3.1.3 ... ... Example 3.1.3 reads as follows:In...
48. A child rolls a marble....Plot graphs etc.

Homework Statement Serway Physics Section 2.4 Accerleration 16. A child rolls a marble on a bent track that is 100 cm long as shown in Figure P2.16. We use x to represent the position of the marble along the track. On the horizontal sections from x=0 to x=20 cm and from x=40 cm to x=60 cm, the...
49. Graphing Derivatives: Concavity and Inflection Points

Homework Statement Hi all. I have a question in regards to a few things in regard to using first and second derivatives to sketch graphs. My math is a little rusty as I was on a 9 day long field trip sleeping in a tent so I am fairly out of practice and can't seem to think this one through too...
50. 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...