Biprimitive Graphs of Smallest Order
نویسندگان
چکیده
A regular and edge-transitive graph which is not vertex-transitive is said to be semisymmetric. Every semisymmetric graph is necessarily bipartite, with the two parts having equal size and the automorphism group acting transitively on each of these parts. A semisymmetric graph is called biprimitive if its automorphism group acts primitively on each part. In this paper biprimitive graphs of smallest order are determined.
منابع مشابه
Finite vertex-primitive and vertex-biprimitive 2-path-transitive graphs
This paper presents a classification of vertex-primitive and vertex-biprimitive 2-path-transitive graphs which are not 2-arc-transitive. The classification leads to constructions of new examples of half-arc-transitive graphs.
متن کاملAn infinite family of biprimitive semisymmetric graphs
A regular and edge transitive graph which is not vertex transitive is said to be semisymmetric Every semisymmetric graph is necessarily bipartite with the two parts having equal size and the automorphism group acting transitively on each of these two parts A semisymmet ric graph is called biprimitive if its automorphism group acts prim itively on each part In this paper a classi cation of bipri...
متن کاملFINITE 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 کاملTHE FINITE VERTEX-PRIMITIVE AND VERTEX-BIPRIMITIVE s-TRANSITIVE GRAPHS FOR s ≥ 4
A complete classification is given for finite vertex-primitive and vertex-biprimitive s-transitive graphs for s ≥ 4. The classification involves the construction of new 4-transitive graphs, namely a graph of valency 14 admitting the Monster simple group M, and an infinite family of graphs of valency 5 admitting projective symplectic groups PSp(4, p) with p prime and p ≡ ±1 (mod 8). As a corolla...
متن کاملGraphs with smallest forgotten index
The forgotten topological index of a molecular graph $G$ is defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $gamma=1,2$, the first through<br /...
متن کامل