Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...

The fractional covering number r* of a hypergraph H (V, E) is defined to be the minimum possible value of ,, v t(x) where ranges over all functions t: V which satisfy ,xe t(x) >= for all edges e e E. In the case of ordinary graphs G, it is known that 2r*(G) is always an integer. By contrast, it is shown (among other things) that for any rational p/q >= 1, there is a 3-uniform hypergraph H with-...

a r t i c l e i n f o a b s t r a c t Keywords: Graph algorithms Simple-path convexity Simple-path convex hull Totally balanced hypergraphs In a connected hypergraph a vertex set X is simple-path convex (sp-convex, for short) if either |X| 1 or X contains every vertex on every simple path between two vertices in X (Faber and Jamison, 1986 [7]), and the sp-convex hull of a vertex set X is the mi...

We make the following three observations regarding a question popularized by Katznelson: is every subset of $${\mathbb {Z}}$$ which set Bohr recurrence also topological recurrence? (i) If G countable abelian group and $$E\subseteq G$$ an $$I_0$$ set, then $$E-E$$ recurrence. In particular $$\{2^n-2^m : n,m\in {\mathbb {N}}\}$$ (ii) Let {Z}}^{\omega }$$ be direct sum countably many copies with s...

Let d and t be fixed positive integers, and let K t,...,t denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem of extremal hypergraph theory, due to Erdős [7], the number of hyperedges of a d-uniform hypergraph on n vertices that does not co...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

An automorphism α of a Cayley graph Cay(G,S) of a group G with connection set S is color-preserving if α(g, gs) = (h, hs) or (h, hs−1) for every edge (g, gs) ∈ E(Cay(G,S)). If every color-preserving automorphism of Cay(G,S) is also affine, then Cay(G,S) is a CCA (Cayley color automorphism) graph. If every Cayley graph Cay(G,S) is a CCA graph, then G is a CCA group. Hujdurović, Kutnar, D.W. Morr...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

Cayley graph is a graph constructed out of a group Γ and a generating set A ⊆ Γ. When Γ = Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir(n, A). In this paper, we attempt to find the total domination number of Cir(n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir(n, A). Further, it is proved that Cir(n, A) is 2-total exc...

A t − (n, k, ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in exactly of the edges (blocks). A partial t − (n, k, ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in at most edges; or equivalently the intersection of every set of + 1 blocks contains fewer than t elements. Let us denote by f (n, k, t) ...