1
vote
0answers
37 views

How we show primitive action shows alternating group

I have a graph (as shown in figure), which represents a quotient of the group $$G=\langle A,B,C,D; A^3=B^2=C^3=D^2=(AC)^2=(AD)^2=(BC)^2=(BD)^2=1 \rangle.$$ I proved that $G$ acts 2-transitively and so ...
4
votes
1answer
37 views

Graph with sharply 1-transitive automorphism group

What finite Graphs $G$ have the property that for all $v,w\in G$, there is exactly one automorphism $\phi$ of $G$ with $\phi(v)=w$? Of course, each of the three graphs with one or two vertices have ...
0
votes
1answer
78 views

Arc transitivity of the complete graph

Recall that a graph $G$ is arc transitive if the natural action of $\mathrm{Aut}(G)$ on $A(G) = \{ (u,v) | \{u,v\} \in E(G)\}$ is transitive. In other words, given $(u,v),(u'.v') \in A(G)$ one finds ...
4
votes
1answer
299 views

Orbits of adjacency matrices under conjugation by permutation matrices.

(Disclaimer: I am new here, so be patient with my mistakes, but I welcome corrections, advice or comments.) I am interested in if anyone knows of ways of characterizing the orbits of an adjacency ...