We study the approximability of the weighted edge-dominating set problem. Although even the unweighted case is NP-Complete, in this case a solution of size at most twice the minimum can be efficiently computed due to its close relationship with minimum maximal matching; however, in the weighted case such a nice relationship is not known to exist. In this paper, after showing that weighted edge ...

For a given graph H and n ≥ 1, let f(n,H) denote the maximum number m for which it is possible to colour the edges of the complete graph Kn with m colours in such a way that each subgraph H in Kn has at least two edges of the same colour. Equivalently, any edge-colouring of Kn with at least rb(n,H) = f(n,H) + 1 colours contains a rainbow copy of H. The numbers f(n,H) and rb(Kn, H) are called an...

Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe conditions that (i) $sum_{xin N^-(v)}f(x)ge 1$ and$sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, where $N^-(v)$(resp. $N^+(v)$) consists of all in-neighbors (resp.out-neighbors) of $v$, and (...

A subset M of the edges a graph G is matching if no two in are incident. maximal that not contained larger matching. S vertices with isolated total dominating set every vertex adjacent to at least one S. Let µ*(G) and γt(G) be minimum cardinalities G, respectively. δ(G) denote degree G. We observe ≤ 2µ*(G) when 1 2 − + ≥ 3. show upper bound for domination number tight fixed δ(G). provide constr...

We provide a new direct proof of the ℓ 2 \ell ^2 -boundedness Discrete Spheri...

Virtual backbone has been used extensively in various aspects for wireless ad hoc or sensor networks recently. We propose an approximation solution to construct a virtual backbone based on a more generalized and realistic model of polynomial bounded growth. A localized distributed algorithm of MCDS_GBG for computing a Minimum Connected Dominating Sets as backbone in the growth-bounded graph is ...

Gillis, Todd E., Christian R. Marshall, Xiao-Hua Xue, Thor J. Borgford, and Glen F. Tibbits. Ca binding to cardiac troponin C: effects of temperature and pH on mammalian and salmonid isoforms. Am J Physiol Regulatory Integrative Comp Physiol 279: R1707–R1715, 2000.—A reduction in temperature lowers the Ca sensitivity of skinned cardiac myofilaments but this effect is attenuated when native card...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.