Arc‐transitive bicirculants

نویسندگان

چکیده

In this paper, we characterise the family of finite arc-transitive bicirculants. We show that every bicirculant is a normal r $r$ -cover an graph lies in one eight infinite families or seven sporadic graphs. Moreover, each these ‘basic’ graphs either circulant, and latter case has for some integer .

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A classification of cubic bicirculants

The well-known Petersen G(5, 2) admits a semi-regular automorphism α acting on the vertex set with two orbits of equal size. This makes it a bicirculant. It is shown that trivalent bicirculants fall into four classes. Some basic properties of trivalent bicirculants are explored and the connection to combinatorial and geometric configurations are studied. Some analogues of the polycirculant conj...

متن کامل

Decompositions of complete multipartite graphs

This paper answers a recent question of Dobson and Marušič by partitioning the edge set of a complete bipartite graph into two parts, both of which are edge sets of arctransitive graphs, one primitive and the other imprimitive. The first member of the infinite family is the one constructed by Dobson and Marušič.

متن کامل

Locally 3-Arc-Transitive Regular Covers of Complete Bipartite Graphs

In this paper, locally 3-arc-transitive regular covers of complete bipartite graphs are studied, and results are obtained that apply to arbitrary covering transformation groups. In particular, methods are obtained for classifying the locally 3-arctransitive graphs with a prescribed covering transformation group, and these results are applied to classify the locally 3-arc-transitive regular cove...

متن کامل

Quartic half-arc-transitive graphs with large vertex stabilizers

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m

متن کامل

Arc-transitive regular cyclic covers of the complete bipartite graph

Characterizing regular covers of edge-transitive or arc-transitive graphs is currently a hot topic in algebraic graph theory. In this paper, we will classify arctransitive regular cyclic covers of the complete bipartite graph Kp,p for each odd prime p. The classification consists of four infinite families of graphs. In particular, such covers exist for each odd prime p. The regular elementary a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of the London Mathematical Society

سال: 2022

ISSN: ['1469-7750', '0024-6107']

DOI: https://doi.org/10.1112/jlms.12504