A subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt (G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected. The connected domination number γc(G) of G is the minimum cardinality taken over all min...

We prove that every (claw, net)-free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, 3nds either a dominating pair or an induced doubly dominating cycle. We show also how one can use structural properties of (claw, net)-free graphs to solve e4ciently the domination, indep...

In this paper, we consider graphs having a unique minimum independent dominating set. We first discuss the effects of deleting a vertex, or the closed neighborhood of a vertex, from such graphs. We then discuss five operations which, in certain circumstances, can be used to combine two graphs, each having a unique minimum independent dominating set, to produce a new graph also having a unique m...

We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T , there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.

Global Rainbow Thermometry is presented. It is a new technique for measuring average size and temperature of spray droplets. For data inversion, a global rainbow pattern is employed, which is formed by constructive interference of laser-light scattering spherical droplets. The non-spherical droplets and liquid ligaments provide a uniform background and thus do not influence the interference pat...

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core a(12) and the thickness of the coating δ are varied. As the ratio δ/a(12) increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/a(12) ≲ 10(-3), the rainbow intensity is ...

Dichloroacetate selectively improves cardiac function and metabolism in female and male rainbow 1 trout 2 3 Pavan K. Battiprolu* and Kenneth J. Rodnick 4 5 6 Department of Biological Sciences, Idaho State University, Pocatello, ID 83209-8007 7 8 *Current address: Department of Metabolic disorders, Amgen, Inc. South San Francisco, CA 94568. 9 10 Corresponding author. e-mail: [email protected]; ph...

Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...

Battiprolu PK, Rodnick KJ. Dichloroacetate selectively improves cardiac function and metabolism in female and male rainbow trout. Am J Physiol Heart Circ Physiol 307: H1401–H1411, 2014. First published September 12, 2014; doi:10.1152/ajpheart.00755.2013.— Cardiac tissue from female rainbow trout demonstrates a sex-specific preference for exogenous glucose and glycolysis, impaired Ca handling, a...

Motivation Want to learn a combinatorial parameter of a graph: the maximum matching size the independence number α(G), the minimum vertex cover size, the minimum dominating set size Krzysztof Onak – Sublinear Graph Approximation Algorithms – p. 2/32 Motivation Want to learn a combinatorial parameter of a graph: the maximum matching size the independence number α(G), the minimum vertex cover siz...