In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k 6= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs...

More than forty years ago, Erdős conjectured that for any t ≤ nk , every k-uniform hypergraph on n vertices without t disjoint edges has at most max {( kt−1 k ) , ( n k ) − ( n−t+1 k )} edges. Although this appears to be a basic instance of the hypergraph Turán problem (with a t-edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify t...

in this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. also, we represent several theorems for constructing each generalized skew t-normal distribution. next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, nickel and vanadium, associated with crude oil in shadgan wetland in the south-...

A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we establish a necessary condition on n for there to exist a t-subset-regular selfcomplementary k-uniform hypergraph with n vertices. In addition, we show that this necessary condition is also sufficient in the case k = 3 and t...

In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two nonnormal connected cubic arc-transitive Cayley graphs for finite nonbelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.

For a positive integer s, a graph Γ is called s-arc transitive if its full automorphism group AutΓ acts transitively on the set of s-arcs of Γ . Given a group G and a subset S of G with S = S−1 and 1 / ∈ S, let Γ = Cay(G, S) be the Cayley graph of G with respect to S and G R the set of right translations of G on G. Then G R forms a regular subgroup of AutΓ . A Cayley graph Γ = Cay(G, S) is call...

Linde, Moore, and Nordahl introduced a generalisation of the honeycomb dimer model to higher dimensions. The purpose this article is describe number structural properties generalised model. First, it shown that samples are in one-to-one correspondence with perfect matchings hypergraph. This leads Kasteleyn theory: partition function equals Cayley hyperdeterminant adjacency hypermatrix Second, w...

In this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. Also, we represent several theorems for constructing each generalized skew t-normal distribution. Next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, Nickel and Vanadium, associated with crude oil in Shadgan wetland in the south-...