The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

CONVEXITY RELATED ISSUES FOR THE SET OF HYPERGRAPHIC SEQUENCES Hasmik Sahakyan, Levon Aslanyan Abstract: We consider ( ), the set of all degree sequences of simple hypergraphs with vertices and hyperedges. We show that ( ), which is a subset of the -dimensional + 1-valued grid , is not a convex subset of ; and give a characterization of the convex hull of ( ).

Let k be a positive integer and G = (V,E) be a connected graph of order n. A set D ⊆ V is called a k-dominating set of G if each x ∈ V (G) − D is within distance k from some vertex of D. A connected k-dominating set is a k-dominating set that induces a connected subgraph of G. The connected k-domination number of G, denoted by γ k(G), is the minimum cardinality of a connected k-dominating set. ...

Let k be a positive integer and let G = (V,E) be a simple graph. The k-tuple domination number γ×k(G) of G is the minimum cardinality of a k-tuple dominating set S, a set that for every vertex v ∈ V , |NG[v]∩S| ≥ k. Also the total k-domination number γ×k,t(G) of G is the minimum cardinality of a total k -dominating set S, a set that for every vertex v ∈ V , |NG(v)∩S| ≥ k. The k-transversal numb...

In this paper we present fixed-parameter algorithms for the problem Dual—given two hypergraphs, decide if one is the transversal hypergraph of the other—and related problems. In the first part, we give algorithms for the parameters number of edges of the hypergraphs, the maximum degree of a vertex, and vertex complementary degrees. In the second part, we use an Apriori approach to obtain FPT re...

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [Mil], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one ...

We prove that a (recursively) enumerable degree is contiguous i it is locally distributive. This settles a twenty-year old question going back to Ladner and Sasso. We also prove that strong contiguity and contiguity coincide, settling a question of the rst author, and prove that no m-topped degree is contiguous, settling a question of the rst author and Carl Jockusch [11]. Finally, we prove som...

The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both the relative randomness and the relative computational power of real numbers. This paper proves that the computable Lipschitz degrees of computably enumerable sets are not dense. An immediate corollary is that the Solo...

The existence of isolated degrees was proved by Cooper and Yi in 1995 in [6], where a d.c.e. degree d is isolated by a c.e. degree a if a < d is the greatest c.e. degree below d. A computably enumerable degree c is non-isolating if no d.c.e. degree above c is isolated by c. Obviously, 0 is a non-isolating degree. Cooper and Yi asked in [6] whether there is a nonzero non-isolating degree. Arslan...