Related papers: Automorphism Groups of the Pancake Graphs
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
We prove that every connected strongly regular graph on sufficiently many vertices is Hamiltonian. We prove this by showing that, apart from three families, connected strongly regular graphs are (highly) pseudo-random. Our results suggest a…
We define a grid graph $G$ as a Cartesian product of path-graphs $P_n$ or cycle-graphs $C_n$ as shown in Figure 1, and we ask, when can the edge set of a complete graph be expressed as a disjoint union of graphs isomorphic to $G$? That is,…
In this paper, all graphs are assumed to be finite. For $s\geq 1$ and a graph $\G$, if for every pair of isomorphic connected induced subgraphs on at most $s$ vertices there exists an automorphism of $\G$ mapping the first to the second,…
Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity and leaves models unable to capture long-range relationships.…
A non-planar graph is almost-planar if either deleting or contracting any edge makes it planar. A graph with $n$ vertices is pancyclic if it contains a cycle of every length from $3$ to $n$, and it is Hamiltonian if it contains a cycle of…
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…
To construct a Paley graph, we fix a finite field and consider its elements as vertices of the Paley graph. Two vertices are connected by an edge if their difference is a square in the field. We will study some important properties of the…
We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with maximum number of automorphisms for their genus and survey geometric realization of pentagonal…
Every finitely generated self-similar group naturally produces an infinite sequence of finite $d$-regular graphs $\Gamma_n$. We construct self-similar groups, whose graphs $\Gamma_n$ can be represented as an iterated zig-zag product and…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
In this paper we characterize "large" regular graphs using certain entries in the projection matrices onto the eigenspaces of the graph. As a corollary of this result, we show that "large" association schemes become $P$-polynomial…
As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
The structure of the automorphism group of the sandwich semigroup IS_n is described in terms of standard group constructions.
Adinkras are a graphical tool for studying off-shell representations of supersymmetry. In this paper we efficiently classify the automorphism groups of Adinkras relative to a set of local parameters. Using this, we classify Adinkras…
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…
There has been a rising interest in graph neural networks (GNNs) for representation learning over the past few years. GNNs provide a general and efficient framework to learn from graph-structured data. However, GNNs typically only use the…
Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…
A graph $\G$ is {\em symmetric} or {\em arc-transitive} if its automorphism group $\Aut(\G)$ is transitive on the arc set of the graph, and $\G$ is {\em basic} if $\Aut(\G)$ has no non-trivial normal subgroup $N$ such that the quotient…