منابع مشابه
FINITE s-ARC TRANSITIVE GRAPHS OF PRIME-POWER ORDER
An s-arc in a graph is a vertex sequence (α0, α1, . . . , αs) such that {αi−1, αi} ∈ EΓ for 1 6 i 6 s and αi−1 6= αi+1 for 1 6 i 6 s− 1. This paper gives a characterization of a class of s-transitive graphs; that is, graphs for which the automorphism group is transitive on s-arcs but not on (s+ 1)-arcs. It is proved that if Γ is a finite connected s-transitive graph (where s > 2) of order a p-p...
متن کاملANALYSING FINITE LOCALLY s-ARC TRANSITIVE GRAPHS
We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...
متن کاملTwo-geodesic transitive graphs of prime power order
In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...
متن کاملFinite Transitive Permutation Groups and Finite Vertex-Transitive Graphs
The theory of vertex-transitive graphs has developed in parallel with the theory of transitive permutation groups. In this chapter we explore some of the ways the two theories have influenced each other. On the one hand each finite transitive permutation group corresponds to several vertex-transitive graphs, namely the generalised orbital graphs which we shall discuss below. On the other hand, ...
متن کاملnormal edge-transitive and $frac{1}{2}-$arc$-$transitive cayley graphs on non-abelian groups of order $2pq$, $p > q$ are odd primes
darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p, where $p$ is a prime number, sci. china math., 56 (1) (2013) 213-219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$. in this paper we continue this work by classifying the connected cayley graph of groups of order...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2000.2012