相关论文: Strongly regular graphs decomposable into a divisi…

This article considers a strongly regular graph with parameters (2048,276,44,36) that is related to the extended binary Golay code. That graph is known since about 1975 but there seems to be not much information on the contained maximal…

We determine new upper bounds for the clique numbers of strongly regular graphs in terms of their parameters. These bounds improve on the Delsarte bound for infinitely many feasible parameter tuples for strongly regular graphs, including…

In 2002, D. Fon-Der-Flaass constructed a prolific family of strongly regular graphs. In this paper, we prove that for infinitely many natural numbers $n$, this family contains $n^{\Omega(n^{2/3})}$ strongly regular $n$-vertex graphs $X$…

Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W.~Kantor's non-classical $\mathrm{GQ}(5^2,5)$, are stumbling stones for existing…

In this paper, we prove the existence of directed strongly regular graphs with parameters $(63,11,8,1,2)$. We construct a pair of nonisomorphic dsrg(63,11,8,1,2), where one is obtained from the other by reversing all arrows. Both directed…

We show that hyperplane sections of strongly formal manifolds inherit strong formality. In particular, this property holds for generalized complete intersections defined by positive line bundles with trivial first de Rham cohomology group.…

Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph…

Strongly regular graphs are highly symmetrical and can be described fully with just a few parameters, yet the existence of many of them is still under the question. In this paper, we continue the study of the famuly of strongly regular…

The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification…

A $k$-regular graph on $v$ vertices is a {\em divisible design graph} if there exist integers $\lambda_1,\lambda_2,m,n$ such that the vertex set can be partitioned into $m$ classes of size $n$ and any two different vertices from the same…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions…

It is proved that if a graph is regular of even degree and contains a Hamilton cycle, or regular of odd degree and contains a Hamiltonian $3$-factor, then its line graph is Hamilton decomposable. This result partially extends Kotzig's…

Let $\lambda\geq2$ be an integer. For strongly regular graphs with parameters $(v, k, a,c)$ and smallest eigenvalue $-\lambda$, Neumaier gave two bounds on $c$ by using algebraic property of strongly regular graphs. In this paper, we will…

Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…

We prove the existence of directed strongly regular graphs with parameters (60,21,11,6,8), (60,22,12,8,8), (60,24,10,9,10), (60,25,17,8,12), (60,27,21,12,12) and (60,28,20,14,12). The group $S_5 \times 2$ acts transitively on the…

An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, \lambda, t)$ is described. A computer program was used to find the initial digraphs. The remaining…

We use finite incident structures to construct new infinite families of directed strongly regular graphs with parameters \[(l(q-1)q^l,\ l(q-1)q^{l-1},\ (lq-l+1)q^{l-2},\ (l-1)(q-1)q^{l-2},\ (lq-l+1)q^{l-2})\] for integers $q$ and $l$ ($q,…

We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural ``limit object'', namely a symmetric measurable 2-variable…

It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). In this paper, we investigate whether the spectra of higher order Laplacians associated with these graphs can…