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...

Rainbow connection number rc(G) of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we show that for every connected graph G, with minimum degree at least 2, the rainbow connection number is upper bounded by γc(G) + 2, where γc(G) is th...

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...

A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

A two-valued function f defined on the vertices of a graph G = (V,E), f : V → {−1, 1}, is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. That is, for every v ∈ V, f(N(v)) ≥ 1, where N(v) consists of every vertex adjacent to v. The weight of a total signed dominating function is f(V ) = ∑ f(v), over all vertices v ∈ V . The total ...

A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k-Dominating Set, or (2) produces a dominating set of size at most g(k), where g(k) is some fixed function of k. Such an outcome is termed an FPT approximation algorithm. We describe some results that begin to provide some answers. We show that there is n...

Let G = (V,E) be a nontrivial, finite, and connected graph. A function c from E to {1,2,...,k},k ∈ N, can considered as rainbow k-coloring if every two vertices x y in has an x- path. Therefore, no path's edges receive the same color; this condition is called “rainbow path”. The smallest positive integer k, designated by rc(G), connection number. Thus, k-coloring. Meanwhile, strong within for h...

A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident to v. Wang and Li conjectured that for k > 4, every edge-colored graph with minimum color degree at least k contains a rainbow matching of size at least ⌈k/2⌉. We prove the slightly weaker statement that a rainbow matching...

In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of Kn, there is a rainbow path on (3/4− o(1))n vertices, improving on the previously best bound of (2n + 1)/3 from [?]. Similarly, a k-rainbow path in a proper...

A function f de1ned on the vertices of a graph G = (V; E); f :V → {−1; 0; 1} is a minus dominating function if the sum of its values over any closed neighborhood is at least one. The weight of a minus dominating function is f(V ) = ∑ v∈V f(v). The minus domination number of a graph G, denoted by −(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bo...