After posting a question in graph-symmetries, I realized that the tag got kind of mixed up. Any ideas how to solve this...? Do we need 2 tags? For currently 10 questions...

"According to a strengthened version of Frucht's theorem, there are infinitely many asymmetric cubic graphs." If there are any, what is the smallest cubic bipartite asymmetric graph? Kind of a bipartite version of Frucht's graph. If there are none, why's that? EDIT: The graph doesn't necessaril...

I'm programming something, but I'm stuck at something which more math-oriented people probably can help me with. I am giving a polyhedron in the following form: for each vertex I get the cyclic order of the neighbors around that vertex. I am also given the complete automorphism group (so not onl...

On the basis of this definition: Two graphs are equivalent if they have the same set of edges (ex. (A,B),(A,C)) how would you determine equivalence for graphs that are not labelled: ex.

$$\frac{6x-5}{3x+1}$$ How do you write this in the form $$\frac{b}{x+c} + a$$ I know how to find a (2) by asymptote theory, but I don't know how to re-arrange to find B.

I have a binary string $l=(l_1,l_2,\ldots,l_{2n})$ with $l\in\{0,1\}$ and the conditions $l_i \cdot l_{i+n}=0$ for all $i$ and $\sum l_i=n$. Now, I was wondering how many distinct string exist, when a string is equivalent to another string by the transformations $$(l_1,l_2,\ldots,l_{2n})\to(l_{2n...

Let $G$ be an undirected, connected graph without loops. Let's call $G$ symmetric iff it has a non-trivial automorphism (that is a permutation $\pi : V(G) \rightarrow V(G) $ – which is not the identity permutation – that preserves the edge relation). Further, let us denote the set of fix points ...

I have tried to impose Hermitian symmetry on the complex number $z$ which is varies with $x$. I need to take its inverse Fourier transform. A hermitian symmetry should give a real valued inverse FT. $$ \operatorname {Re} (x) = \sinh[c\cdot \log(x)]/[\cosh[c\cdot \log(x)] + \cos(c)] $$ $$ ...

Determine the amount of automorphisms in the group $\operatorname{Aut}(H)$ where $H$ is the graph with 6 points and five lines in the shape of a capital 'H'. Here is what it should look like, I labeled the points: Now I can clearly see that rotation through the line $12$ and rotation through a...

A function $f(x)$ that fulfills $f(x)=\pm f(-x)$ is called (a)symmetric even/odd. How do you call functions that fulfill $f(x)=\color{blue}\pm f(\color{red}\pm 1/x)$? "$\color{red}{\text{Positive/Negative}}$ Reciprocal $\color{blue}{\text{(anti)symmetric}}$"..? edited according to the com...

I would like a good hint for the following problem that takes into account the position at which I am stuck. The problem is as follows Let $\mathbb{Z}_n$ be the cyclic group of order $n.$ Find a simple graph $G$ such that $\mathrm{Aut}(G) = \mathbb{Z}_n.$ The book that I am studying sugges...

I posted this answer here: http://math.stackexchange.com/a/1121698/205062 My answer was commented upon by someone who misunderstood it but that comment (the second comment) has attracted two upvotes. I find it very rude to misconstrue my post and then pour further salt in the wounds by upvoting ...