Mader conjectured that for all ` there is an integer δ(`) such that every digraph of minimum outdegree at least δ(`) contains a subdivision of a transitive tournament of order `. In this note we observe that if the minimum outdegree of a digraph is sufficiently large compared to its order then one can even guarantee a subdivision of a large complete digraph. More precisely, let ~ G be a digraph...

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph Kn , a lexicographic product [K̄b], a deleted lexicographic product [K̄b] − b , where ...

An important aspect of cryptography with matrices is that given N ×N matrix P over a field F find a class of matrices G over F such that the associated doubly circulant matrix Gc is singular in order that the equation AGB = P in circulant matrices A,B has infinitely many solutions. The aim of this note is to present such a class of matrices G. We also present a direct method of finding the inve...

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorph...

In this paper a new approach to the modelling of ATM-traffic is proposed. The traffic is measured and characterised by its first and second order statistic moments. A Markov Modulated Poisson Process (MMPP) is used to capture the information in these two stochastic moments. Instead of a general MMPP, a circulant MMPP is used to reduce the computational cost. A circulant MMPP (CMMPP) is an MMPP ...

In this paper we study defensive alliances in some regular graphs. We determine which subgraphs could a critical defensive alliance of a graph G induce, if G is 6-regular and the cardinality of the alliance is at most 8. In particular, we study the case of circulant graphs, i.e. Cayley graphs on a cyclic group. The critical defensive alliances of a circulant graph of degree at most 6 are comple...

This paper explores dense Gaussian Networks, which are interconnection networks based on dense Circulant graphs of degree four. Gaussian networks exhibit better distance related characteristics than equivalent topologies such as Tori. We will show that the Gaussian integers, or the set of complex numbers with integer coefficients, constitute the appropriate mathematical model to deal with these...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent set of vertices (if u, v ∈ N , u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l). A k-kernel is a (k, k − 1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are g...

In this paper we answer the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer. The network is described by a circulant graph G, which is characterized by its circulant adjacency matrix A. Formally, we say that there exists a perfect state transfer (PST) between vertices a, b ∈ V (G) if |F (τ)ab| = 1, for some positive real number τ ...