How can I show that the Petersen graph is not a Cayley graph?  I don't know very much about Cayley graphs, I know that they are vertex-transitive, but so is the Petersen graph. It probably has to do with the group structure of $\Gamma$ in $Cay(\Gamma,S)$ (which is a group of order $10$, i.e., it is either the cyclic group $C_{10}$ or the dihedral group $D_{10}$). Then I am guessing we go for some sort of contradiction(?). My group theory is a bit rusty, I would very much appreciate someone showing me how to do this one!
On the  it is mentioned that it is not a Cayley graph.    How it this proved? Honestly I don't even know how to start this. The only criteria I can think of is that all vertices must have the same degree. Also the degree being odd should imply that one generator of the group has order 2. But then how do I proceed?  Edit: As already mentioned in the comments, the link did not answer my question.
How do question bookmarks work? Where does the word "torsion" in algebra come from? Unable to install Springseed 2 on Ubuntu 15.04 Unicode applies the convention of using a  as signature at the beginning of a text stream, identifying the encoding used within it. The following three bytes at the beginning of a file: EF BB BF, identifies this file as a UTF8 file. Vi and most text editors gracefully ignore this signature. Open office does that as well, but it adds this signature at the beginning.  Now, if I open a TeX file with OpenOffic.org, and I do that quite a lot (for mixed directionality editing), the signature is added, and baffles LaTeX, which produces an error message such as:   ! LaTeX Error: Missing \begin{document}.   See the LaTeX manual or LaTeX Companion for explanation.  Type  H &lt;return&gt;  for immediate help.  ...                                                l.1   ��\documentclass{article}   whereas a simple dump of the file does not show the problem. Is there a way to eliminate this problem, while staying in the realm of latex? Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous. Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty$. Prove that $f$ is uniformly continuous.   Since $f(x)\to 0$ as $x\to \pm\infty$ we have $|f(x)|&lt;\epsilon $ whenever $x&lt;-K$ and $x&gt;K$ where $K&gt;0$.  Also $f$ is uniformly continuous on $[-K,K]$ as the domain is compact.  Hence $f$ is uniformly continuous in $(-\infty,-K)\cup [-K,K]\cup (K,\infty)$.  But how to conclude that $f$ is uniformly continuous on $\Bbb R$ from above as I may chose $x\in (-\infty,-K);y\in [-K,K]$ ,how to conclude that $|f(x)-f(y)|&lt;\epsilon $ from above for a given $\epsilon$?  Please suggest the edits required. How to make table split in two pages I am writing a paper using the elsarticle document class. However, the article contains a long table which is sent to the next page, in the middle of the page although I have specified the position as 'here'. Is there any way to make the table split if one page is not long enough for the table? Thank you very much for your very kind help. gpgkeys: key C927EBE00F1B0520 not found on keyserver Possible Duplicate:    I am using 10.04 LTS - Lucid Lynx. I shutdown the computer while a software update was running. Then after I restarted my computer and while the update manager was running, I got this error:  Could not download all repository indexes The repository may no longer be available or could not be contacted because of network problems. If available an older version of the failed index will be used. Otherwise the repository will be ignored. Check your network connection and ensure the repository address in the preferences is correct. GPG error: http://toolbelt.herokuapp.com ./ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY C927EBE00F1B0520 Failed to fetch  http://ppa.launchpad.net/rabbitvcs/ppa/ubuntu/dists/**DISTRIBUTION**/main/binary-i386/Packages.gz 404  Not Found   I went through the answers to  and I tried this $ sudo launchpad-getkeys  Please wait... launchpad-getkeys is running an update so it can detect the missing GPG keys Trying to import all the missing keys gpg: requesting key 0F1B0520 from hkp server keyserver.ubuntu.com gpgkeys: key C927EBE00F1B0520 not found on keyserver gpg: no valid OpenPGP data found. gpg: Total number processed: 0 launchpad-getkeys has finished importing all missing GPG keys.  Try running sudo apt-get update - you shouldn't see any key  errors anymore  But when I run sudo apt-get update again, it again shows that the key was not found on the keyserver. How to solve this problem? I am trying to do a clean install of the octave3.2 package.   To do this, I removed it, then tried to reinstall it.   When I reinstalled, an error occurred. It could be a bug in the package, but I want to make sure I have everything removed so that I can do a clean install.  Is it enough to do this?  sudo apt-get --purge remove octave3.2 bash fork: retry: Resource temporarily unavailable I am trying to run a shell script which will create process using a shell script. I get Resource temporarily unavailable error. how to identify which limit (memory/process/filecount) is creating this problem. Below is my ulimit -a results.  core file size          (blocks, -c) 0 data seg size           (kbytes, -d) unlimited scheduling priority             (-e) 0 file size               (blocks, -f) unlimited pending signals                 (-i) 563959 max locked memory       (kbytes, -l) unlimited max memory size         (kbytes, -m) unlimited open files                      (-n) 65535 pipe size            (512 bytes, -p) 8 POSIX message queues     (bytes, -q) 819200 real-time priority              (-r) 0 stack size              (kbytes, -s) unlimited cpu time               (seconds, -t) unlimited max user processes              (-u) 10000000 virtual memory          (kbytes, -v) unlimited file locks                      (-x) unlimited How to show that $\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3?$ Given the integral $(1)$     $$\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3\tag1$$   This integral seems to be quite tough, I can't even know where to start. I have try substitution $u=1+\cos^3 x$ and $u=\cos^3 x$, can seem to remove the x variables.  We have the following identities   $$\sin^5a={5\over 8}\sin a-{5\over 16}\sin 3a+{1\over 16}\sin 5a\tag2$$  $$\cos^3 a={3\over 4}\cos a+{1\over 4}\cos 3a\tag3$$  We may write $(1)$ as  $$\int_{0}^{\pi}{\sin x(1-\cos^2 x)^2\over 1+\cos x(1-\sin ^2 x)}\mathrm dx\tag4$$  $u=1-\sin^2 x\implies \mathrm du=-2\sin x\cos x\mathrm dx$ then $(4)$ becomes  $${1\over 2}\int_{0}^{1}{(1-u)^2\over \sqrt{u}+u^2}\mathrm du\tag5$$  $u=v^2\implies du=2vdv$ then $(5)$ becomes  $$\int_{0}^{1}{(1-v^2)^2\over v+v^4}\cdot{v\mathrm dv}\tag6$$ Simplify to  $$\int_{0}^{1}{(1-v)(1-v^2)\over 1-v+v^2}\mathrm dv\tag7$$  I guess using partial decomposition of fraction and integrate term by term, seem lengthy process  How else can we prove $(1)$? I put all my music on a playlist seperate from the rest of the music on the iTunes library, so I could easily get to what music I wanted to listen to, instead of my brother or sister's music. My brother recently got an iPod nano, and didn't know how to use iTunes, after explaining it to him, he deleted my whole entire playlist. I didn't know, so when I hooked my phone up to the computer to sync some songs I was going to buy, all the music on my phone disappeared. I've tried re-doing the playlist and syncing all of it to my phone again, but it won't work. I've also tried turning off my phone for certain periods of time, still nothing.  I lost about 200 songs (thankfully not more), and I don't know how to get it back. I'm new to Linux but not to app development. I come from a RealBasic on a Mac background.   I've accepted that I need to learn a new language to develop for Linux (since RB won't run on 64 bit distros and is a cloed proprietary language) but I want to make sure I pick the right one.   I've been looking at Python and was all set to go until I read that PyGTK is becoming obsolete with the introduction of GTK 3. Is this true? The Ubuntu developer website stills seems to recommend it with Glade for the UI but I want to make sure that I don't learn something that's on the way out! Can Yoda pilot a starfighter? In a trailer for Kinect Star Wars, I saw Yoda driving a Jungle Speeder and that got me wondering. Can and has Yoda ever piloted a starfighter?  During the Clone Wars, it seems plausible that they could commission a small-sized green Jedi starfighter. Is their any indication that he has piloting experience? Western Digital drive making beeping noise Keyboard layout/language changes in every boot Please stop bounties from turning off community moderation Possible Duplicate:                tl;dr: Please get rid of "This question has an open bounty and cannot be closed"  Questions with bounties on them can't be closed:    This is by design, and the recommended course of action is to flag for moderator attention, at which point they'll decide whether to refund the bounty and close the question or not.   But why should a bounty disable regular community moderation?  We should be able to cast close votes on bountied questions as usual, and if a question gets enough, the bounty's refunded and the question closed.  An obvious benefit would be reduced burden on moderators, but I doubt that this is really a significant part of their workload.  More important is allowing the entire community's wisdom to be brought to bear.  Consider this question:      Having a simple MFC application with web browser controller that navigates to some site and then to another one on and on.      Using a powerfull machine (16 cores and lots of memory) OS is Server 2008 R2. I can see when launching my app over 30 instances I'm getting the OS UI (each window including my app, mspaint, taskmgr etc..) become very sluggish and slow.      I have monitored the machine resources (CPU, memory and GDI objects) but it seems that all of them are not even close to be in some level of stress.      What is the problematic resource that influence the machine in such way?      10x, Guy   It doesn't look like a good question: somewhat poorly written, vague, not a ton of information, etc.  I would vote to close this question.  However, I don't do much work with MFC and maybe there's something I'm missing.  (I can readily imagine a similarly bad looking question with the extremely concrete answer: .)  I'm comfortable casting a vote to close, not closing unilaterally.  Flagging for a moderator just passes the buck to them, when the correct action is letting the community weigh in. Here is a sentence excerpted from ,     Teen suicide is a growing health concern. It is the third-leading cause of death for young people ages 15 to 24, surpassed only by homicide and accidents, according to the U.S. Center for Disease Control and Prevention.   I've heard people use both "people aged from X to Y" and "people ages from X to Y" quite often, but I've always been believing that only the former is grammatically correct, whereas in the latter the "ages" doesn't seem to serve as any grammatical component of this sentence. So when I see an APA paper use "ages" in that way, I am just quite surprised: I just can't believe such an authoritative and rigourous academic institution will let such an explicit (and indeed naive, even to a non-native speaker's eyes) grammatical mistake survive in their publications. I'm aware that in daily language usage one ought not to become so fussy over insignificant matters like this, but I do wonder whether it should be paid attention to in academic writings.  OR, using "ages" in that way is no longer considered a grammatical mistake? Honestly I don't think this'd be true, but if it really is, I'd be grateful to be informed. Thanks! I saw this several times in different movies, but I don't understand what is this supposed to mean. The main idea is when the scene is about to change, for one second or so we still see the picture from the old scene, but the sound is already coming from from the upcoming scene. Why do they do this? What's the purpose of this technique? What is the datatype of facebook userid Select all columns except one in MySQL? I'm trying to use a select statement to get all of the columns from a certain MySQL table except one. Is there a simple way to do this?  EDIT: There are 53 columns in this table (NOT MY DESIGN)