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...

A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.

We give lower bounds on the maximum possible girth of an r-uniform, d-regular hypergraph with at most n vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute constant factor (viz., by a factor of between 3/2 + o(1) and 2 + o(1)). We also define a random r-uniform ‘Cayley’ hypergraph on the symmetric group Sn which has girth Ω...

We show that an n-vertex hypergraph with no r-regular subgraph has at most 2n−1 + r− 2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraph having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.

Let D(n)(D(n, k)) denote the maximum possible d such that there exists a d-regular hypergraph (d-regular k-uniform hypergraph, respectively) on n vertices containing no proper regular spanning subhypergraph. The problem of estimating D(n) arises in Game Theory and Huckemann and Jurkat were the first to prove that it is finite. Here we give two new simple proofs that D(n), D(n, k) are finite, an...

This study investigates the domination, double and regular domination in intuitionistic fuzzy hypergraph (IFHG), which has enormous application computer science, networking, chemical, biological engineering. Few properties of IFHG are established. Furthermore, definitions complement independent set given. The relation between an its was discussed. Moreover, illustrated by determining containmen...

In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, with equality only if the hypergraph is regular. Here, we prove a wider class of inequalities in a ...

Recently, Storm [8] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi...