Related papers: Locally s-distance transitive graphs and pairwise …
We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $\Lambda$ and a "code" assigned to each orbit of…
We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We…
We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi-Civita connection of a Riemannian…
In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of…
In this note, we study non-transitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasi-isometric regular…
In this paper we construct structures from Mathieu group $M_{11}$. We classify transitive $t$-designs with 11, 12 and 22 points admitting a transitive action of Mathieu group $M_{11}$. Thereby we proved the existence of designs with…
In this work, we explore edge direction, transitivity, and connectedness of Cayley graphs of gyrogroups. More specifically, we find conditions for a Cayley graph of a gyrogroup to be undirected, transitive, and connected. We also show a…
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
In [Distrance-regular Cayley graphs on dihedral groups, J. Combin. Theory Ser B 97 (2007) 14--33], Miklavi\v{c} and Poto\v{c}nik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of…
The paper is devoted to generalizations of actions of topological groups on manifolds. Instead of a topological group, we consider a local topological group generalizing the notion of a~germ or a~neighborhood in a topological group. The…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
The problem of constructing or characterizing strongly regular Cayley graphs (or equivalently, regular partial difference sets) has garnered significant attention over the past half-century. In 2003, Miklavi\v{c} and Poto\v{c}nik [European…
A $k$-regular graph on $v$ vertices is a {\em divisible design graph} if there exist integers $\lambda_1,\lambda_2,m,n$ such that the vertex set can be partitioned into $m$ classes of size $n$ and any two different vertices from the same…
We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive tilings. We characterize these…
A Cayley graph $\Cay(G,S)$ is said to be inner-automorphic if $S$ is a union of conjugacy classes of a group $G$, and arc-transitive if its full automorphism group acts transitively on the set of arcs. In this paper, we characterize four…
The characterization of distance-regular Cayley graphs originated from the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. In this paper, a classification of distance-regular Cayley…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
In this paper we investigate graphs that admit a group acting arc-transitively such that the local action is semiprimitive with a regular normal nilpotent subgroup. This type of semiprimitive group is a generalisation of an affine group. We…
Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal.,…