A class of symmetric graphs with 2-arc-transitive quotients

Details A class of symmetric graphs with 2-arc-transitive quotients A class of symmetric graphs with 2-arc-transitive quotients

2009-05-31

arxiv.org/abs/0906.0154v1

Mathematics

Combinatorics

22 pages

Scientific paper

Let $\Gamma$ be a finite X-symmetric graph with a nontrivial X-invariant partition $\mathcal {B}$ on $V(\Gamma)$ such that $\Gamma_{\mathcal {B}}$ is a connected (X,2)-arc-transitive graph and $\Gamma$ is not a multicover of $\Gamma_{\mathcal {B}}$. This article aims to give a characterization of $(\Gamma, X, \mathcal {B})$ for the case where $|\Gamma(C) \cap B| = 3$ for $B\in \mathcal {B}$ and $C \in \Gamma_{\mathcal {B}}(B)$. This investigation requires a study on (X,2)-arc-transitive graphs of valency 4 or 7. We give a characterization of tetravalent (X,2)-arc-transitive graphs at first; and as a byproduct, we prove that every tetravalent (X,2)-transitive graph is either the complete graph on 5 vertices or a near n-gonal graph for some $n\ge 4$. Then we show that a heptavalent $(X,2)$-arc-transitive graph $\Sigma$ can occur as $\Gamma_{\mathcal {B}}$ if and only if $X_\tau^{\Sigma(\tau)}\cong PSL(3,2)$ for $\tau\in V(\Sigma)$.

Affiliated with

Also associated with

No associations

Rating

A class of symmetric graphs with 2-arc-transitive quotients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A class of symmetric graphs with 2-arc-transitive quotients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A class of symmetric graphs with 2-arc-transitive quotients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-708614