Intereting Posts

Closed-form of integral $\int_0^1 \int_0^1 \frac{\arcsin\left(\sqrt{1-s}\sqrt{y}\right)}{\sqrt{1-y} \cdot (sy-y+1)}\,ds\,dy $
Given an exponential generating function, is it possible to isolate only the even terms?
Review of my T-shirt design
Is the submodule of a finitely generated free module finitely generated?
Eigenvalues of $AB$ and $BA$
How to prove $\sum\limits_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$?
If the graphs of $f(x)$ and $f^{-1}(x)$ intersect at an odd number of points, is at least one point on the line $y=x$?
Why can 2 uncorrelated random variables be dependent?
Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
Integrating $\int\frac{x^3}{\sqrt{9-x^2}}dx$ via trig substitution
Finding $\dfrac{d^nx}{dy^n}$
The Chinese Remainder Theorem for Rings.
Difference between functional and function.
Maximizing $\frac{x(1-f(x))}{3-f(x)}$
calculating angle in circle

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!

- Software for generating Cayley graphs of $\mathbb Z_n$?
- Cayley graphs on small Dihedral and Cyclic group
- Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$
- Name for Cayley graph of a semigroups?

- Motivation for spectral graph theory.
- For a Planar Graph, Find the Algorithm that Constructs A Cycle Basis, with each Edge Shared by At Most 2 Cycles
- Proving a triangle with different edge colors exists in a graph.
- Consequences of cycle space cut space duality
- Cover time chess board (king)
- In a graph, connectedness in graph sense and in topological sense
- Euler's formula for tetrahedral mesh
- Which directed graphs correspond to “algebraic” diagrams?
- How many 2-edge-colourings of $K_n$ are there?
- Find cycles in graphs which do not contain other cycles

Let $ P\simeq Cay(G,S)$, then $|S|=3$ and $|G|=10$, then $G\simeq \mathbb{C_{10}}$ or $\mathbb{D_{10}}$, in both cases $G$ has cycle order 4, whereas $P$ has cycle of or 5.

- How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$
- Is the $n$-th prime smaller than $n(\log n + \log\log n-1+\frac{\log\log n}{\log n})$?
- Does the integral $\int_0^\infty \sin(2x^4) \, dx$ converge absolutely/conditionally?
- Proof of Neumann Lemma
- What parameters can be used to tell a least squares fit is “well fit”?
- Inverse of a Function exists iff Function is bijective
- A formal name for “smallest” and “largest” partition
- how prove $\sum_{n=1}^\infty\frac{a_n}{b_n+a_n} $is convergent?
- When can you simplify the modulus? ($10^{5^{102}} \text{ mod } 35$)
- Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
- evaluation of $ \operatorname{Arg}\zeta (1/2+is) $ ??
- An exercise about finite intersection property in $T_1$ space
- Why is $\mathbb{Q}(t,\sqrt{t^3-t})$ not a purely transcendental extension of $\mathbb{Q}$?
- How to find complex numbers $z,\lambda,\mu$ such that $(z^\lambda)^\mu\neq z^{\lambda\mu}$
- How many arrangements of a bookshelf exist where certain books must be to the left/right of other books?