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.
Is there any good software which plots 3d graphs and vectors. I just want to plot linear 3d graphs and vectors in 3d. I don't mind paying for this but it should be reliable and easy to use.
I've a graph similar to a 1/x^2 function, but it's only represents positive X values. The Y axis represents the duration in seconds, and X represents the number of objects. This graph shows that, as the number of objects grows, the time decreases.
If I want to represent this graph in a semi-log...
I have a set of measured data. I need to plot this in MATLAB and show two graphs in one plot.
Data for first graph is : [0.35,0],[0.4,130],[0.45,400],[0.5,0.11],[0.55,34] and so on.
Second graph is a function.
So, how to plot sequence of data in matlab? Which command should I use?
Hi all I have a confusion regarding a physics concept. When you consider area under graph (velocity time graph), if the area is below x axis, is the area considered to be negative?
For example, look at the attachment. There are 2 shaded areas. Let the area above x-axis be A and area below...
Homework Statement
...Bounded by graphs of equations:
z=xy,
z=0,
y=x,
x=1
I don't know what z=xy is. The rest of boundaries are clear.
I assume that when y=1 and x=1, z=1. But, is this a z=1 plane?
Check my figure attached.
Thank you.
Homework Equations
The Attempt at a Solution
Homework Statement
How many complete bipartite graphs have n vertices?
Homework Equations
The Attempt at a Solution
I said, let the first bipartition set have x vertices and the second bipartition set have y vertices. So x+y=n.
I think that you would do C(n, x)*C(n-x...
I think this is probably the right place to put it, didn't really fit anywhere else.
I've got the joyless task of writing a lab report at university and need to put a graph in it, ideally with error bars. I don't have a problem with error bars normally, but I'm coming unstuck about what to do...
Homework Statement
I have multiple 1D data sets, let's call them data1, data2, data3, etc. Each data set has the same number of entries. Each one is either a row or a column (I can just use Transpose[...], so same] and when I use the ListPlot[] function, I get a graph where the vertical axis...
Is there another name for "the volume Swept through" in maths "Graphs" ?
Is there another name for "the volume Swept through" in maths "Graphs" ?
No matter how and where I search I can't find anything showing me how to get the "the volume swept through" of a graph and yet they ask it just...
I want to plot a 3D graph.
A solid graph and a wireframe mesh graph.
What are the different ways to do it in this script.
The variables i want to be plotted in this script are 'pic' 'TSFC' 'NonFs'.
Dont mind the working, everything is correct. The only matter of concern is the 3d graph and...
Prove by induction on the number of edges in a graph that any bipartite graph has edge colouring number equal to its maximum valency. Also, Find such an edge colouring for a bipartite 4-regular cartesian or tensor product of your choice of 2-regular graphs
Prove that if a weighted graph has unique weights on each edge that there is only 1 minimum spanning tree. Do I need to use an algorithm such as Prim's to show this or do I use properties of weighted graphs?
1. Determine the equation y=f(x) for each of the following cases in simplest form. All of the plots are straight lines and all coordinates are indicated with abscissa first, ordinate second (x,y).
-log y versus log x on a rectilinear graph passes through (5,7) and (2,3)
-(y-2)^2 versus x...
Homework Statement
Graphs A and B are entries to a NOR gate with 2 inputs. Draw the output C.
Graphs X and are entries to a XOR gate. Draw the output Z.
Homework Equations
The Attempt at a Solution
Homework Statement
A string with mass density u = 9.00 g/m extends from zero to infinity along the x-axis. It is
under tension T = 25 N, and is driven by a mechanism at x = 0.
The velocity of the drive mechanism depends on time as:
vy(t) =
0 (if t = 0)
10.0 cm/s (if 0 < t ≤ 0.1 s)...
In class, we have been introduced to the supremum and infimum concepts and shown them on graphs, but I am wondering how to go about deriving them, and determining if they are part of the set, without actually having to graph them- especially for more complicated sets.
Velocity-Vs Time Graphs -- 2nd problem
How would i sketch a velocity vs time graph for the following scenario:
A ball is thrown up out of a person's hand, it rises and then returns to the person's hand.
I just don't know how to illustrate this on a velocity vs time graph
Thanks
A person starts 50m [N] of a reference point then walks until hs is 50m [S] of the reference point. The person then jogs until he is 50m [N] of the ref. point. The person then runs until he is at the ref. point.
How do i sketch a velocity vs time graph and an acceleration vs time graph for...
So the problem is that i have a physics test coming up and its about forces and graphs.
The teacher can not explain the different formulas clearly which results in everyone getting bad grades. I wonder if anyone can explain this to me.Homework Equations
A RCXD (a little car with explosives...
Hi,
I'm working on an assignment which requires me to superimpose the graphs of 10 different discontinuous functions on the same graph. Can someone please explain step-by-step how to do so in MAPLE? By the way, I have absolutely no experience in any computer programming in any form and I've...
Hey everyone. Sorry to post another topic, but i thought this would be easy to find on google, to help me with , but i can't find it.
All I am really lookin for is someone to let me know if my answers are right, and if not, then how i can fix them :)
Anyways, i was asked to graph...
I was coming up with examples for my students as to why we demand they actually understand math in calculus class instead of plugging all their functions into their graphing calculators to draw graphs and calculate integrals. I basically hit the motherload... I have confirmed this works on...
Homework Statement
Marian who is standing on her balcony is surprised by a pigeon, and throws a flowerpot up, in the air at 2.1 m/s. It takes a total of 3 s for the flowerpot to smash to the ground. The flowerpot experiences acceleration due to gravity of 9.8m/s
a) How high is Marians...
Homework Statement
f(x) = ex2
find the range of f(x)
How do I do this - I don't know how to draw this graph?g(x) = x2 + 3ex2
Again, how is this done without drawing the graph?Homework Equations
The Attempt at a Solution
so for the first graph, for example, I differentiated it
dy/dx for f(x) =...
(note for editor; this is not a homework problem, this is bred out of my desire to visualize 3space)
Hello fellows,
I am hoping that somebody can help me. I've asked multiple teachers and tutors, but nobody can solve my seemingly very easy problem.
I am taking a course in multivariable...
Hi everyone, I need a lot help on how to find automorphisms on these particular Cayley graphs.
I have three groups here: <a,b,c,d | [ab,cd]=1>; <a,b,c,d | abcda^(-1)b^(-1)c^(-1)d^(-1)=1>; <a,b,c,d | [a,b][c,d]=1>.
I finally got three Cayley graphs down, first one is like Z^2, but with...
Holy...I have to retype my entire post *sigh* lovely.
Ok, let's try a shorter version. I've had a question that my engineering cousin was unable to help me with (perhaps too busy). I'm a programmer first, and barely remember Calculus I so we're both on the same page.
Let's start with y=x...
Hi, I have been representing complex numbers in graphical form in school recently. My teacher was telling me about a graph which shows all 4 quadrants and basically shows you what each quadrant is in terms of pi. Hopefully you understand what I mean, I have been looking on the internet for this...
The Following data table provides information about a crate of radishes that is sliding down the ramp of a delivery truck
time position
0 ------ 0
2------ 0.6
4-------2.4
6------- 5.4
8------- 9.6
10------ 15Next it asks you to draw a position time graph, which i did, and its identical...
Homework Statement
In my A2 maths class, we were doing revision on transformations of graphs, as in:
Homework Equations
with a graph f(x)
af(x) is a stretch scale factor a in the y-direction
f(bx) is a stretch scale factor 1/b in the x-direction
f(x)+c is a translation of c in the y-...
hello..here is a program..
and i need to make a graph of tcentre(i) against t(i)..how to do this...
these variables are bold in the below code
!here are the declaration of variables
DIMENSION...
Homework Statement
how would I draw the graph
f(x) = ln|3x-6|
Homework Equations
NONE
The Attempt at a Solution
So I know that the graph ln(3x-6) would be a transformation of ln(x) 6 units to the right and the stretch by scale factor (1/3) along the x-axis (i.e: divide all x...
Hello everyone, thanks for reading my post.
Issue 1:
Example:
Suppose I want to draw a graph for sec θ=x + 1/4x
I want 'θ' on the y-axis and different values of 'x' on x-axis. Can I plot the graph using Matlab?
Issue 2: I want to know if it's possible to plot graph of complex mathematical...
¿Software to simulate graphs?
Is there an alternative to MATLAB for simulating equations,
I am looking for a way of getting some intuition for some Convection Diffusion Equation. I would like to play around with it, simulate it, change its IC/BCs, having some interactive graphs and stuff.
Does anyone know if there is a software program that I can find/buy somewhere that can
recognize an image of a curve and generate a 2D Cartesian equation for it?
In my line of work I am constantly referencing these regular 2d graphs (power vs resistance graphs for thermoelectric modules)...
Homework Statement
I have an issue with Straight Line graphs, I have never done them before (I touched on them in Seconday School, y=mx+c that sort of stuff) Now I've been faced with a problem that I need to learn. It's not homework it's revision but I thought it was more relevant to post here...
How does higher order derivatives affect the graph? Mostly just the 3rd, 4th or 5th derivatives. I believe I have found the 3rd one but I'm not sure about it or the others.
Hello All, This problem comes from #18 of section 4.3 out of stewarts 6th edition.
The Question:
Consider the following function:
f(x)= e^(-x) * sqrt(x)
What I am trying to find.
a.) Find the intervals on which f is increasing and decreasing.
b.) find any relative extrema.
c.)...
i have an excel file containing 2 graphs [R & V], and their x & y coordinates in 4 separate lists [the X coordinates of R, the X coordinates of V, the Y coordinates of R, the Y coordinates of V]
i need to calculate the X & Y coordinates of a 3rd graph through a weighted formula that takes 55%...
Homework Statement
Firstly I'm sorry to bother all of you that will find this question really basic but I haven't studied Maths since GCSE 7 years ago and I am now doing a degree in Engineering without A Level Maths so any help would be great...I need to work out the algebra and the main...
Homework Statement
Prove that almost all graphs are not planar graphs.
Homework Equations
Kuratowski's Theorem
The Attempt at a Solution
Kuratowski's Theorem states that a graph is planar if and only if it does not contain a subgraph homeomorphic to K5 or K3,3. Therefore, if I...
Homework Statement
Let G be a random graph on n vertices:
1) What is the expected number of triangles in G?
2) What is the variance in the number of triangles?
Homework Equations
N/A
The Attempt at a Solution
I think I can do (1) by using indicator variables. In particular, let...
Homework Statement
What is the expected slope of the line? What was the actual slope of the line of best fit? Calculate the gravity constant g from the slope of your graph
Homework Equations
k = (Mg) / (y_0 - y)
4pi^2/g x L = T^2
The Attempt at a Solution
I understand how to...
This is a little more open ended then most HW questions. I'm helping a friend with some HW and we need to transform a parabola. Ultimately we have to find the tangent line, vertex, ect but I'm failing to recall the rules on how to manipulate the parabola to be in the domain of the graph we need...
Homework Statement
Hello all, there has been some debate in my class as to the output waveform for the following circuit:
Others say that the output will always be zero.