If, for a subset S of Z, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-valued polynomials and (c) by finitely many k-tuples of polynomials with integer coefficients (variables ranging through the integers in each case), then a ⇒ b (obviously), b ⇒ c, and neither implication is reversible. We...

Let G = (V,E) be an undirected graph and let π = {V1, V2, . . . , Vk} be a partition of the vertices V of G into k blocks Vi. From this partition one can construct the following digraph D(π) = (π,E(π)), the vertices of which correspond one-to-one with the k blocks Vi of π, and there is an arc from Vi to Vj if every vertex in Vj is adjacent to at least one vertex in Vi, that is, Vi dominates Vj ...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...

In this paper we introduced the concepts of global domination number and domatic in product fuzzy graph is denoted by γg(G) dg(G), respectively determine for several classes obtain Nordhaus-Gaddum type results parameter. Further, some bounds dg(G) are investigated. Also relations between γg(G)(dg(G)) other known parameter Product graphs Finally introduce concept full about done.

A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in cite{bhh} as a function$f:V(G)rightarrow{0,1,2,3}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least twoneighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must haveat least one neighbor $u$ with $f(u)ge 2$. The weight of a double R...

Let a tuple of n objects obeying a query graph (QG) be called the n-tuple. The “Ddistancevalue” of this n-tuple is the value of a linear function of distances of the n objects that make up this ntuple, 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 Ddistance-values, the so-called K-Multi-Way Distance...

A t-(v, k,;\) directed design (or simply a t-(v, k, ;\)DD) is a pair (V, B), where V is a v-set and B is a collection of (transitively) ordered k-tuples of distinct elements of V, such that every ordered t-tuple of distinct elements of V belongs to exactly). elements of B. (We say that at-tuple belongs to a k-tuple, if its components are contained in that k-tuple as a set, and they appear with ...