Related papers: Exploring the 3-Token Graph of Particular Graphs
The $2$-token graph $F_2(G)$ of a graph $G$ is the graph whose set of vertices consists of all the $2$-subsets of $V(G)$, where two vertices are adjacent if and only if their symmetric difference is an edge in $G$. Let $G$ be the join graph…
This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which…
This work is divided into two main parts. The first part is devoted to exploring the connectivity of random subgraphs of cartesian products of $K_1$, $K_2$, and $P_3$. In the second part, the author presents a short review of the results…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…
As a vital link between group theory and graph theory, Cayley graphs provide a geometric framework for encoding algebraic structures. This study explores the properties of Cayley graphs derived from cyclic groups whose order is the square…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in [Deniz et al., 2018]. A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid…
In this article we investigate the structure of uniformly $k$-connected and uniformly $k$-edge-connected graphs. Whereas both types have previously been studied independent of each other, we analyze relations between these two classes. We…
In this paper, we prove that every 3-chromatic connected graph, except $C_7$, admits a 3-vertex coloring in which every vertex is the beginning of a 3-chromatic path. It is a special case of a conjecture due to S.~Akbari, F.~Khaghanpoor,…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges, and subgraphs, our metric graph kernels are purely based on…
We investigate graphs that have characteristic-dependent well-covered dimension and show how more of these graphs can be constructed from known ones.
Dvo\v{r}\'ak, Kr\'al' and Thomas gave a description of the structure of triangle-free graphs on surfaces with respect to 3-coloring. Their description however contains two substructures (both related to graphs embedded in plane with two…
The paper investigates connections between abstract polytopes and properly edge colored graphs. Given any finite n-edge-colored n-regular graph G, we associate to G a simple abstract polytope P_G of rank n, called the colorful polytope of…