ARTICLE
TITLE

Finite Edge-Transitive Oriented Graphs of Valency Four: a Global Approach

SUMMARY

We develop a new framework for analysing finite connected, oriented graphs of valency four, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of `basic' graphs such that each graph of this type is a normal cover of at least one basic graph. The basic graphs either admit an edge-transitive group of automorphisms that is quasiprimitive or biquasiprimitive on vertices, or admit an (oriented or unoriented) cycle as a normal quotient. We anticipate that each of these additional properties will facilitate effective further analysis, and we demonstrate that this is so for the quasiprimitive basic graphs. Here we obtain strong restrictions on the group involved, and construct several infinite families of such graphs which, to our knowledge, are different from any recorded in the literature so far. Several open problems are posed in the paper.

PAGES
pp. P1.10

 Articles related

José Aliste-Prieto, Logan Crew, Sophie Spirkl, José Zamora    

This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation. We a... see more


Jordan Mitchell Barrett, Valentino Vito    

For fixed finite graphs GG, HH, a common problem in Ramsey theory is to study graphs FF such that F?(G,H)F \to (G,H), i.e. every red-blue coloring of the edges of FF produces either a red GG or a blue HH. We generalize this study to infinite graphs GG, H... see more


Jakub Przybylo    

A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular sub... see more


Teng Fang, Xin Gui Fang, Binzhou Xia, Sanming Zhou    

A finite graph G\Gamma is GG-symmetric if it admits GG as a group of automorphisms acting transitively on V(G)V(\Gamma) and transitively on the set of ordered pairs of adjacent vertices of G\Gamma. If V(G)V(\Gamma) admits a nontrivial GG-invariant partit... see more


Benedikt Stufler    

We study the asymptotic shape of random unlabelled graphs subject to certain subcriticality conditions. The graphs are sampled with probability proportional to a product of Boltzmann weights assigned to their 22-connected components. As their number of v... see more