相关论文: Construction of directed strongly regular graphs u…

Let $k\ge 1$ be an odd integer, $t=\lfloor {{k+2}\over 4}\rfloor$, and $q$ be a prime power. We construct a bipartite, $q$-regular, edge-transitive graph $C\!D(k,q)$ of order $v \le 2q^{k-t+1}$ and girth $g \ge k+5$. If $e$ is the the…

In this paper, we give a complete description of strongly regular graphs with parameters ((n^2+3n-1)^2,n^2(n+3),1,n(n+1)). All possible such graphs are: the lattice graph $L_{3,3}$ with parameters (9,4,1,2), the Brouwer-Haemers graph with…

We present a method to generate directed acyclic graphs (DAGs) using deep reinforcement learning, specifically deep Q-learning. Generating graphs with specified structures is an important and challenging task in various application fields,…

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…

Answering an open question from 2007, we construct infinite $k$-crossing-critical families of graphs that contain vertices of any prescribed odd degree, for any sufficiently large~$k$. To answer this question, we introduce several…

Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…

Let $p$ be a prime, $e$ a positive integer, $q = p^e$, and let $\mathbb{F}_q$ denote the finite field of $q$ elements. Let $f_i : \mathbb{F}_q^2\to\mathbb{F}_q$ be arbitrary functions, where $1\le i\le l$, $i$ and $l$ are integers. The…

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…

Strongly regular graphs (SRGs) are highly symmetric combinatorial objects, with connections to many areas of mathematics including finite fields, finite geometries, and number theory. One can construct an SRG via the Cayley Graph of a…

The feasibility conditions obtained in a previous report are refined, and used to determine several infinite families of feasible parameters for strongly regular graphs with no triangles. The methods are also used to improve the lower bound…

We provide an abundance of strongly regular graphs (SRGs) for certain parameters $(n, k, \lambda, \mu)$ with $n < 100$. For this we use Godsil-McKay (GM) switching with a partition of type $4,n-4$ and Wang-Qiu-Hu (WQH) switching with a…

We consider a directed acyclic network with multiple sources and multiple terminals where each terminal is interested in decoding the sum of independent sources generated at the source nodes. We describe a procedure whereby a simple…

We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…

A result of Erd\"os and R\'enyi shows that for a fixed integer n almost all graphs satisfy the n-e.c. adjacency property. However, there are few explicit constructions of n e.c. graphs for n > 2, and almost all known families of n-e.c.…

We prove that, for any finite set of minimal $r$-graph patterns, there is a finite family $\mathcal F$ of forbidden $r$-graphs such that the extremal Tur\'an constructions for $\mathcal F$ are precisely the maximum $r$-graphs obtainable…

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…

Given feasible strongly regular graph parameters $(v,k,\lambda,\mu)$ and a non-negative integer $d$, we determine upper and lower bounds on the order of a $d$-regular induced subgraph of any strongly regular graph with parameters…

For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array…

We apply spectral analysis of quotients of the Bruhat-Tits buildings of type $\tilde{A}_{d-1}$ to construct isospectral non-isomorphic Cayley graphs of the finite simple groups $\operatorname{PSL}_d({\mathbb F}_q)$ for every $d \geq 5$ ($d…