Related papers: Construction of Directed Strongly Regular Graphs U…
Duval, in "A Directed Graph Version of Strongly Regular Graphs" [{\it Journal of Combinatorial Theory}, Series A 47 (1988) 71 - 100], introduced the concept of directed strongly regular graphs. In this paper we construct several rich…
Directed strongly regular graphs were introduced by Duval in 1998 as one of the possible generalization of classical strongly regular graphs to the directed case. Duval also provided several construction methods for directed strongly…
The concept of directed strongly regular graphs (DSRG) was introduced by Duval in "A Directed Graph Version of Strongly Regular Graphs" [Journal of Combinatorial Theory, Series A 47(1988)71-100]. Duval also provided several construction…
In 1988, Duval introduced the concept of directed strongly regular graphs, which can be viewed as a directed graph version of strongly regular graphs. Such directed graphs have similar structural and algebraic properties to strongly regular…
In this paper, we introduce orbit matrices of directed strongly regular graphs (DSRGs). Further, we propose a method of constructing directed strongly regular graphs with prescribed automorphism group using genetic algorithm. In the…
The concept of directed strongly regular graphs (DSRG) was introduced by Duval in 1988 \cite{A}.In the present paper,we use representation theory of finite groups in order to investigate the directed strongly regular Cayley graphs.We first…
In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. We also study the above association schemes, their fusions…
The paper shows the existence of a family of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). The adjacency matrices of the found digraphs are composed of $3\times 3$ circulant blocks. The automorphism group of all the…
In this paper we present a method for constructing directed strongly regular graphs with assumed action of an automorphism group. The application of this method leads to first examples of directed strongly regular graphs with parameters…
We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
In this paper,we construct some directed strongly regular Cayley graphs on dihedral groups,these generalizes some earlier constructions.We also characterize some certain directed strongly regular Cayley graphs on dihedral groups…
We construct a strongly regular graph with the parameters (65; 32; 15; 16). The idea is to search for an adjacency matrix that consists of circulant blocks. Equations with such matrices can be reduced to congruences with polynomials…
In this paper, we construct directed strongly regular graphs with new parameters by using partial sum families with local rings. 16 families of new directed strongly regular graphs are obtained and the uniform partial sum families are…
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…
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…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
In this paper we introduce a construction of directed strongly regular graphs from smaller ones using equitable partitions. Each equitable partition of a single DSRG satisfying several conditions leads to an infinite family of directed…
In this paper, we count acyclic and strongly connected uniform directed labeled hypergraphs. For these combinatorial structures, we introduce a specific generating function allowing us to recover and generalize some results on the number of…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…