Power graphs provide an innovative way to visualise and analyse the algebraic structure of finite groups. In a power graph, the elements of a finite group serve as vertices, and an edge is drawn ...

Commuting graphs have emerged as a powerful framework for elucidating complex relationships within finite group theory. In these graphs, vertices typically represent non-central elements of a group, ...

Let $G$ be a (simple) {{< link file="graph.md" display="graph" type="references" >}}. The condition that $V(G)$ be finite allows us to apply methods from finite ...

We prove that given any sequence $G_1, G_2,\ldots$ of graphs, where $G_1$ is finite planar and all other $G_i$ are possibly infinite, there are indices $i,j$ such ...

In this paper, we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for ...

Abstract: We study definability in the first-order theory of graph order: i.e. the set of all isomorphism types of simple finite graphs ordered by either the minor, subgraph or induced subgraph ...

Practice Exam: Uncountable Graph Functions and Bellman-Ford Algorithm This exam is designed to deepen your understanding of graphs by exploring uncountable graphs, and also requires you to implement ...

Abstract: Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although ...