In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. A regular graph with vertices of degree
k
{\displaystyle k}
is called a
k
{\displaystyle k}
‑regular graph or regular graph of degree
k
{\displaystyle k}
. Also, from the handshaking lemma, a regular graph contains an even number of vertices with odd degree.
Regular graphs of degree at most 2 are easy to classify: a 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains.
A 3-regular graph is known as a cubic graph.
A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices.
The complete graph
K
m
{\displaystyle K_{m}}
is strongly regular for any
m
{\displaystyle m}
.
A theorem by Nash-Williams says that every
k
{\displaystyle k}
‑regular graph on 2k + 1 vertices has a Hamiltonian cycle.
I am struggling with Hamiltonian formulation of classical mechanics. I think I have grasped the idea of canonical transformations, including the idea of angle-action variables and invariant tori in phase space. Still, few points seem to elude my understanding...
Let's talk about a particle...
In first part,since every block of 4 consecutive symbol contain at least 2 a's
The answer in notes is given
(aa(a+b)(a+b)+a(a+b)a(a+b)+a(a+b)(a+b)a+(a+b)aa(a+b)+(a+b)a(a+b)a+(a+b)(a+b)aa)+
But this wont be true since if we choose aabbbbaa which is possible according to the above regular...
As the slide says, it's not 50-99 characters so what it is?
Source: https://www3.cs.stonybrook.edu/~pfodor/courses/CSE307/L02_Programming_RE.pdf
Also, please tell me how to learn regular expressions? Recommend some university/any courses to take for learning regular expression for backend...
R=(01+010)*
For it I made the below nfa which i believe seems correct. Plus the tutorials that I am following also make sure it’s correct. Q0 is initial state(forgot to mention in figure).
R=(01)*+(010)*
But idk how to convert this to NFA
What will be languages accepted by this NFA? Won’t...
R=(01+010)*
For it I made the below nfa which i believe seems correct. Plus the tutorials that I am following also make sure it’s correct. Q0 is initial state(forgot to mention in figure)...
When I first read the question, it didn't occur to me that these particles would ever meet or catch up with their neighbors. They are all traveling from one vertex to another with a velocity ##v## and a distance ##a##, all either clockwise or anticlockwise right ?
The question says "Each...
Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or...
can anyone help solve this puzzle regarding regular expressions? I was given this in an interview test from BAE systems cyber security department a few years ago and just came across it again, still haven't managed to get anywhere like an answer. I have tried matching each line of regex to form...
The doubt is about B and C.
b)
n = 4, $C = {I,e^{2\pi/4}}
n = 5, $C = {I,e^{2\pi/5}}
n = 6, $C = {I,e^{2\pi/6}}
Is this right?
c)
I am not sure what does he wants...
If 5 charges (each q) are placed at 5 vertex of a regular hexagon of side a then effectively the electric field at the centre of the hexagon is $$\frac{q}{4\pi\epsilon_0a^2} $$ but the potential is $$\frac{5q}{4\pi\epsilon_0a}$$ but then what about $$V=-\int \textbf{E•dr}$$
Hello,
Light, laser or not, is fundamentally electromagnetic radiation with visible wavelengths. Laser light has both high spatial coherence and temporal coherence (highly monochromatic) while regular light has both very low spatial and temporal coherence. Spatial coherence is not about spectral...
What is the difference between those horns/waveguides and regular metal pieces with a same geometry? Why the microwave companies sell those parts at hundreds and thousands dollars? Why we cannot buy some metal sheets or pipes on McMaster-Carr with very low price and make some microwave...
I know these software packages were discussed a lot in the past, but I have not seen much input from the last couple years.
I have used Matlab for many years, but remember using Maple in University Physics courses many years ago. I'm interested in a software package for symbolic math to use...
I have some questions. Let us assume for these questions that I am using the (- + + +) sign convention.
Firstly, we know that if you have a parameterized curve ξ(s), then you can find the proper time between two events at points s1 and s2 by using this formula (assuming that the curve is...
Hi!
I've just read some articles about the fact that wormhole travel would be slower then taking a "regular space time path" between two hypothetical black holes.
This stunned me as I always thought the Einstein - Rosen Bridge would be connecting two distant points in space in a more direct...
So I was working on solving $(\frac{1}{4900})^{100}$, and I figured the only way to do this neatly is through modular arithmetic.
I found that $4900 \equiv 84 \ (\text {mod 112})$, so I concluded $$\frac{1^{100}}{84^{10}\times84^{10} \ (\text{mod 112})}$$
Which should equal...
Homework Statement
I am self studying automata theory and I found a problem set from an old class I took a few years ago, but I have no clue how to solve the following problem, any help would be appreciated.Suppose we have a regular language ##L \subseteq \{0,1\}^*## and the language ##...
Homework Statement
"Let L be any regular language over an alphabet Σ. Using L, we define
chop(L) = {w : ∃ x, y, z ∈ Σ∗ , xyz ∈ L, w = xz}.
Show that chop(L) is regular or give a counter-example."
Homework Equations
If an NFA that describes the language chop(L) exists, then chop(L) is a...
I suck at geometry, but I have this intuitive notion that the points on the corners of a regular tetrahedron are all equidistant. How do I go about proving this true (or false, if I'm wrong)? Note that the highest geometry class I've taken is high school, but I'm okay with any undergraduate...
Hi all, I have this (nondimensionalised) system of ODEs that I am trying to analyse:
\[
\begin{align}
\frac{dr}{dt}= &\ - \left(\alpha+\frac{\epsilon}{2}\right)r + \left(1-\frac{\epsilon}{2}\right)\alpha p - \alpha^2\beta r p + \frac{\epsilon}{2} \\
\frac{dp}{dt}= &\...
Homework Statement
Determine singular points of given DE. Classify as regular or irregular
(x^3 -2x^2 + 3x)^2 y'' + x(x-3)^2 y' + (-x-1)y = 0
Homework EquationsThe Attempt at a Solution
From the polynomial infront of y'' I get
x^2 (x^2 -2x + 3)^2
right out of the bat I can see that x =...
Homework Statement
Show that ##x^2y''+sin(x)y'-y = 0## has a regular singular point at ##x=0##, determine the indicial equation and it's roots.
Homework Equations
For a DE in the form of ##y''+p(x)y'+q(x)y=0##, if both ##p(x)## and ##q(x)## are not analytic at ##x=x_0##, and both...
Hello Everybody, I am Meaningless and I had this doubt on Newtons laws of gravitation while deriving it. My textbook stated the following derivation 9 for any two masses m1, m2, and radius 'r'
It stated that according to the law of product of masses...
Homework Statement
Let CRYPT be the language of cryptographic expressions of this type that can be generated by the following grammar.
S → E
S → ε
E → E + E
E → E − E
E → SIMPLESUB(E, STRING)
E → VIGENERE(E, STRING)
E → LOCTRAN(E, DIGITS)
E → STRING
In this grammar, the non-terminals...
Let $S_n$ be the sum of lengths of all the sides and all the diagonals of a regular $n$-gon inscribed in a unit circle.
(a). Find $S_n$.
(b). Find $$\lim_{{n}\to{\infty}}\frac{S_n}{n^2}$$
$\tiny{231.13.3.75}$
$\textrm{Imagine $3$ unit spheres
(radius equal to 1) with centers at,}\\$
$\textrm{$O(0,0,0)$, $P(\sqrt{3},-1,0)$ and $Q(\sqrt{3},1,0)$.} \\$
$\textrm{Now place another unit sphere symmetrically on top of these spheres with its center at R.} \\$
$\textrm{a Find the...
A nanofiltration filter has a pore size around 0.001 micron. Reverse osmosis filters have a pore size around 0.0001 micron.
Additionaly, reverse osmosis occurs when a semi-permeable membrane separates solutions of different concentrations so osmotic pressure has to be applied to move water from...
The question is about to derive an approximate expression by regular solution theory, It is difficult for me to find relevant source on this question. However, the question to me is so vague that I do not know how to answer.
What I have tried is to search what the interaction parameter is...
Homework Statement
Let γs : I → Rn, s ∈ (−δ, δ), > 0, be a variation with compact support K ⊂ I' of a regular curve γ = γ0. Show that there exists some 0 < δ ≤ ε such that γs is a regular curve for all s ∈ (−δ, δ). Thus, we may assume w.l.o.g. that any variation of a regular curve consists of...
Homework Statement
Let γ be a regular closed curve in Rn. Show that there is a regular homotopy Γ through closed curves with Γ(−, 0) = γ and Γ(−, 1) an arclength parametrization of γ
Homework EquationsThe Attempt at a Solution
Hey guys,
I just posted another question about homotopy but often...
Homework Statement
Show that regular homotopy of regular curves γ : I → Rn is an equivalence relation, that is:
i) γ ∼ γ (where the symbol ∼ stands for “regularly homotopic”);
ii) γ ∼ γ˜ implies ˜γ ∼ γ;
iii) γ ∼ γ˜ and ˜γ ∼ γˆ implies γ ∼ γˆ (here you have to use a smoothing function)...
This is kind of a silly question. I always get "regular" spaces and "normal" spaces confused in topology. This will be a problem if I am asked on a qualifier to prove something about one of these spaces. Is there any linguistic or historical justification to why a regular space deals with a...
1.
Problem Statement:
For the regular solution model, develop the equations for the compositions of the coexisting phases in a binary system and plot the phase boundary as a function of χ/RT.2. This question stems from Sandler's Introduction to Applied Statistical Thermodynamics.
The Attempt...
Hello all
Let ##m_A: \mathbb{K^n} \rightarrow \mathbb{K^n}: X \mapsto AX## and ##A \in M_{m,n}(\mathbb{K})##
(I already proved that this function is linear)
I want to prove that:
A regular matrix ##\iff m_A## is an isomorphism.
So, here is my approach. Can someone verify whether this is...
Bert and Ernie are running around a regular polygon with x sides, all of length 12m. They start from the same point and run in opposite directions. If Bert is twice as fast as Ernie, how far will Ernie have traveled when they meet?
Homework Statement
Homework Equations
(n-2)*180[/B]The Attempt at a Solution
11.a: 7-2=5, 5*180= 900. 900/7= 128.57 degrees
b. How do you find the unknowns?[/B]
Hello! (Wave)
I want to prove that if $L$ is regular then $L^R=\{ w | w^R \in L \}$ is regular.
I have thought the following:
We suppose that $L$ is regular. Then there is a dfa that recognizes $L$.
Assume that $q_0$ is the starting state and $q_n$ is an accepting state, where $n \in...
On chapter over regular surfaces, In definition 1 point 2. He says that x: U → V∩S is a homeomorphisms, but U⊂ℝ^2 onto V∩S⊂ℝ^3. I am confused, how can it be so!
Hi all,
Cam google web search accepet regular expressions? Especially, I need to search strings with any number between two words, for example: "vehicle runs at XXX km/h".
Thank you
Dear Group,
I have a 30_sec_data.txt with weird characters in it and data.txt with nice numeric in it,
Any one have any ideal to help me convert data from weird to regular data using Matlab.
Thank you,
Best regard,
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High Temperature Low Temperature Duality for the Ising Model on an Infinite Regular Tree
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