Related papers: Distance-regular graphs
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
We study the infinite graph of $n$-dimensional rectangular grid that doesn't appear distance regular and the distance regular colorings of this graph, which are defined as the distance colorings with respect to completely regular codes. It…
Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of (dis)similarity between genomes, and studying the distribution of…
The motion of a graph is the minimal degree of its full automorphism group. Babai conjectured that the motion of a primitive distance-regular graph on $n$ vertices of diameter greater than two is at least $n/C$ for some universal constant…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. (https://link.springer.com/chapter/10.1007%2F3-540-46135-3_31) describes some of the first work for identifying and analyzing row and column…
Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. For example, the study of such networks includes the spread of…
In this paper, we study a question of Hong from 1993 related to the minimum spectral radii of the adjacency matrices of connected graphs of given order and size. Hong asked if it is true that among all connected graphs of given number of…
We study {0,\alpha}-sets, which are sets of unit vectors of $\mathbb{C}^m$ in which any two distinct vectors have angle 0 or \alpha. We investigate some distance-regular graphs that provide new constructions of {0,\alpha}-sets using a…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
We update the table of large undirected graphs with given degree and diameter with results obtained since the publication of the survey by M. Miller and J. \v{S}ir\'{a}\v{n} in the {\em Electronic Journal of Combinatorics} (Dynamic Survey…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications…
A graph is called a $k$-planar unit distance graph if it can be drawn in the plane such that every edge is a unit line segment and is involved in at most $k$ crossings. We investigate $u_k(n)$, the maximum number of edges of such graphs on…
The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin-Lu-Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a…
An embedding of a graph on an orientable surface is orientably-regular (or rotary, in an equivalent terminology) if the group of orientation-preserving automorphisms of the embedding is transitive (and hence regular) on incident vertex-edge…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. Fibonacci cubes are induced subgraphs of hypercubes obtained by restricting the vertex set to those binary strings which do not contain consecutive…
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…