arXiv subjects

Nemanja Poznanovic

Publications and source records attributed to Nemanja Poznanovic.

2 recordsLinked to original sources

arXiv2024

Basic Tetravalent Oriented Graphs of Independent-Cycle Type

The family $\mathcal{OG}(4)$ consisting of graph-group pairs $(Γ, G)$, where $Γ$ is a finite, connected, 4-valent graph admitting a $G$-vertex-, and $G$-edge-transitive, but not $G$-arc-transitive action, has recently been examined using a normal quotient methodology. A subfamily of $\mathcal{OG}(4)$ has been identified as `basic', due to the fact that all members of $\mathcal{OG}(4)$ are normal covers of at least one basic pair. We provide an explicit classification of those basic pairs $(Γ, G)$ which have at least two independent cyclic $G$-normal quotients (these are $G$-normal quotients which are not extendable to a common cyclic normal quotient).

math.CO↗

arXiv2024

Basic Tetravalent Oriented Graphs with Cyclic Normal Quotients

Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(Γ, G)$ where $Γ$ is finite, 4-valent, connected, and $G$-oriented ($G$-half-arc-transitive). A subfamily of $\mathcal{OG}(4)$ has recently been identified as `basic' in the sense that all graphs in this family are normal covers of at least one basic member. In this paper we provide a description of such basic pairs which have at least one $G$-normal quotient which is isomorphic to a cycle graph. In doing so, we produce many new infinite families of examples and solve several problems posed in the recent literature on this topic. This result completes a research project aiming to provide a description of all basic pairs in $\mathcal{OG}(4)$.

math.CO↗