Let G be a (p, q)-graph with edge domination number γ′ and edge domatic number d′. In this paper we characterize connected graphs for which γ′ = p/2 and graphs for which γ′ + d′ = q + 1. We also characterize trees and unicyclic graphs for which γ′ = bp/2c and γ′ = q −∆′, where ∆′ denotes the maximum degree of an edge in G.

Let a tuple of n objects obeying a query graph (QG) be called the n-tuple. The “Ddistance-value” of this n-tuple is the value of a linear function of distances of the n objects that make up this n-tuple, according to the edges of the QG. This paper addresses the problem of finding the K n-tuples between n spatial datasets that have the smallest Ddistancevalues, the so-called K-Multi-Way Distanc...

The domatic number of a graph G, denoted dom(G), is the maximum possible cardinality of a family of disjoint sets of vertices of G, each set being a dominating set of G. It is well known that every graph without isolated vertices has dom(G) ≥ 2. For every k, it is known that there are graphs with minimum degree at least k and with dom(G) = 2. In this paper we prove that this is not the case if ...

We investigate the theoretical feasibility of near-optimal, distributed sleep scheduling in energyconstrained sensor networks with pairwise sensor redundancy. In this setting, an optimal sleep schedule is equivalent to an optimal fractional domatic partition of the associated redundancy graph. We present a set of realistic assumptions on the structure of the communication and redundancy relatio...

For k ≥ 1, we consider interleaved k-tuple colorings of the nodes of a graph, that is, assignments of k distinct natural numbers to each node in such a way that nodes that are connected by an edge receive numbers that are strictly alternating between them with respect to the relation <. If it takes at least χint(G) distinct numbers to provide graph G with such a coloring, then the interleaved m...

Top-k query is an efficient way to show the most important objects to user from massive amounts of data. After huge effort working on database performance, recently, an explain capability has attract more attention in recent years. In top-k query, since people may not specify his/her accurate preference, he may feel frustrated with the top-k results and propose a question such that “why my expe...

In order to update k-anonymous and confidential database, the suppression based and generalization based updating protocol technique has been proposed. These protocols check whether the database inserted with the new tuple is still k anonymous without knowing the content of the table and database respectively. But these methods will not work if initial database is empty. Also, if the incoming t...

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...