Related papers: Exploring the 3-Token Graph of Particular Graphs
We study the properties of finite graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to some fixed graph $F$. This is a natural extension of the study of regular graphs, and of the study of graphs of…
In this paper, we study the unit graph $ G(\mathbb{Z}_n) $, where $ n $ is of the form $n = p_1^{n_1} p_2^{n_2} \dots p_r^{n_r}$, with $ p_1, p_2, \dots, p_r $ being distinct prime numbers and $ n_1, n_2, \dots, n_r $ being positive…
Data-driven analysis of large social networks has attracted a great deal of research interest. In this paper, we investigate 120 real social networks and their measurement-calibrated synthetic counterparts generated by four well-known…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…
We study $c$-crossing-critical graphs, which are the minimal graphs that require at least $c$ edge-crossings when drawn in the plane. For $c=1$ there are only two such graphs without degree-2 vertices, $K_5$ and $K_{3,3}$, but for any fixed…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
Strongly chordal graphs are a subclass of chordal graphs. Farber also established a number of different characterisations for this class of graphs. These include an intersection graph characterisation that is analogous to a similar…
Graph theory is a promising approach in handling the problem of estimating the connectivity probability of vehicular ad-hoc networks (VANETs). With a communication network represented as graph, graph connectivity indicators become valid for…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases…
A vertex colouring of a graph $G$ is "nonrepetitive" if $G$ contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively…
We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…