Recent content by Bingk1

Thanks! I'll give it a few more days, but from what I've read so far, it seems like there's no official name for the type of graph I'm concerned with...maybe we can put up a vote for it, hehehe.

Makes sense, will consider fractional graph also. As for pseudograph being used for multigraphs, actually, I had never heard of pseudographs until this naming issue came up. It seems like because there are variations in the definition of a multigraph (i.e. allowing for loops or not), pseudograph...

Hello, Just wondering if any of you have encountered a term for a particular type of graph. It is like a graph that allows for loops, but for loops, instead of joining a vertex to itself, it joins a vertex to nothing. I just want to be consistent with existing terminology, if there are none...

Hello, I need help finding all non-isomorphic graphs that have exactly ten vertices, and each vertex has degree three. Does anyone know where I could find them? Or how many there are? I know that playing around with generalized Petersen graphs gives a few, but I doubt that would give all of...

Thanks to all who viewed my post and spent some time on it! But ... after giving it much thought, I realized that posing the question in terms of graphs might lead to a solution in graph theory, and after some investigation, the solution is the Erdos-Gallai Theorem.

Hello, I need some ideas on this problem, but there's a bit of an explanation before I get to the actual problem. Say you have C couples to be arranged over N tables. Rules for arrangement are as follows: 1) Couples may not be seated in the same table (i.e. the husband and wife must be...

I got stuck on that one too, that's why I couldn't proceed. I thought I'd get into trouble with higher powers, so I didn't check those. Thanks again! Just curious, is there any method you're using to factorize the polynomial? I'm basically doing a systematic guessing, is there any other way?

Re: X^(2n) + x + 1 is reducible over Z2 for n>2 2^{n} I tried editing the title, but it didn't save the change

If n \geq 3, prove that x^{2^n} + x + 1 is reducible over \mathbb{Z}_2. Not sure how to go about this. I was thinking it might involve induction. For n=3, we have x^8+x+1=(x^2+x+1)(x^6+x^5+x^3+x^2+1), but I can't find any pattern to help with the induction. Thanks in advance!

Hello, I found this question, and I was able to do the easier parts, but I'm really not comfortable with automorphisms in fields. Let f(x)=x^2 + 1 = x^2 - 2 \in Z_3[x]. Let u= \sqrt{2} be a root of f in some extension field of Z_3. Let F=Z_3(\sqrt{2}). d)List the automorphisms of F which leave...

Thank you! I didn't think to consider the function h ... but it should've occurred to me.

Hi, that's actually what I got, but I'm pretty sure I got it the wrong way. I don't remember exactly what I did (the exam wasn't returned to us), but my method involved the Maximum Modulus Principle (sort of like applying Liouville's on open balls). How exactly is that a consequence of...

Hello, this was another question on the exam which I wasn't sure about: Let f and g be entire such that |f(z)| \leq |g(z)| \ \forall z \in \mathbb{C}. Find a relationship between f and g. I'm kinda lost on this one... Thanks!

Hello, This was an exam question which I wasn't sure how to solve: Suppose f is entire and |f(z)| \leq C(1+ |z|)^n for all z \in \mathbb{C} and for some n \in \mathbb{N}. Prove that f is a polynomial of degree less than or equal to n. I know that f can be expressed as a power series, but I'm...

Hello, I'm trying to read a paper titled "Cluster Identification in Nearest Neighbor Graphs". It's a mixture of probability, graph theory, and topology. I'm having difficulty interpreting some of the ideas, specially when it comes to k nearest neighbor graphs. I've been trying to look for a...