a r t i c l e i n f o a b s t r a c t A graph Γ is k-CS-transitive, for a positive integer k, if for any two connected isomorphic induced subgraphs A and B of Γ , each of size k, there is an automorphism of Γ taking A to B. The graph is called k-CS-homogeneous if any isomorphism between two connected induced subgraphs of size k extends to an automor-phism. We consider locally-finite infinite k-...

A generalization of some of the Folkman's constructions [13] of the so called semisymmetric graphs, that is regular graphs which are edgebut not vertex-transitive, was given in [22] together with a natural connection of graphs admitting 12 -arc-transitive group actions and certain graphs admitting semisymmetric group actions. This connection is studied in more detail in this paper. In Theorem 2...

The existence of a connected 12-regular {K4,K2,2,2}-ultrahomogeneous graph G is established, (i.e. each isomorphism between two copies of K4 or K2,2,2 in G extends to an automorphism of G), with the 42 ordered lines of the Fano plane taken as vertices. This graph G can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of K4 and as the edge-disjoint union of 21 in...

Let G be a group with socle a simple group of Lie type defined over the finite field with q elements where q is a power of the prime p. Suppose that G acts transitively upon the lines of a linear space S. We show that if p is significant then G acts flag-transitively on S and all examples are known. MSC(2000): 20B25, 05B05. 1 Background and statement of result A linear space S is an incidence s...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

The existence of a connected 12-regular {K4, K2,2,2}-ultrahomogeneous graph G is established, (i.e. each isomorphism between two copies of K4 or K2,2,2 in G extends to an automorphism of G), with the 42 ordered lines of the Fano plane taken as vertices. This graph G can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of K4 and as the edge-disjoint union of 21 i...

A generalization of some of Folkman’s constructions (see (1967) J. Comb. Theory, 3, 215–232) of the so-called semisymmetric graphs, that is regular graphs which are edgebut not vertex-transitive, was given by Marušič and Potočnik (2001, Europ. J. Combinatorics, 22, 333–349) together with a natural connection between graphs admitting 1 2 -arc-transitive group actions and certain graphs admitting...

Abstract We explore the possibilities for elementary embeddings $j : M \to N$ , where and N are models of ZFC with same ordinals, $M \subseteq has access to large pieces j . construct commuting systems such maps between countable transitive that isomorphic various canonical linear partial orders, including real line ${\mathbb R}$