相关论文: Directed Strongly Regular Cayley Graphs on Dihedra…
In this paper, we characterize some certain directed strongly regular Cayley graphs on Dihedral groups $D_{n}$, where $n\geqslant 3$ is a positive integer.
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…
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…
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…
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…
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…
Let $p$ be an odd prime, and $D_{2p}=\langle \tau,\sigma\mid \tau^p=\sigma^2=e,\sigma\tau\sigma=\tau^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to…
In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group $D_n=\langle a,b\mid a^n=b^2=1,bab=a^{-1}\rangle$. Moreover, we also obtain some simple sufficient conditions for the…
In [Distrance-regular Cayley graphs on dihedral groups, J. Combin. Theory Ser B 97 (2007) 14--33], Miklavi\v{c} and Poto\v{c}nik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of…
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…
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…
In this note, we give the Hamiltonian decomposition of the Cayley graph on the dihedral group $D_{2p}$ where $p$ is a prime.
In this paper, we classify reflexible regular Cayley maps for dihedral groups.
Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [J.A Davis, Partial difference sets in p-groups, Arch.Math.63 (1994) 103-110; K.H Leung, S.L. Ma, Partial difference sets with Paley…
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…
This paper investigates the enumeration of Cayley digraphs, focusing on counting Cayley digraphs on dihedral groups up to CI-isomorphism. By leveraging the Cauchy-Frobenius Lemma and properties of automorphisms, we derive an explicit…
Let $p$ be an odd prime, and $D_{2p}=\langle a,b\mid a^p=b^2=1,bab=a^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we completely classify the cubic Cayley graphs on $D_{2p}$ up to isomorphism by means of spectral method. By…
A Cayley hyper-digraph is a directed hypergraph that its automorphism group contains a subgroup acting regularly on vertices and a Cayley hypermap is a hypermap whose automorphism group contains a subgroup which induces regular action on…
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 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…