On the Cartesian product of non well-covered graphs

A graph is well-covered if every maximal independent set has the same cardinality, namely the vertex independence number. We answer a question of Topp and Volkmann and prove that if the Cartesian product of two graphs is well-covered, then at least one of them must be well-covered

A bound on the size of a graph with given order and bondage number

AbstractThe domination number of a graph is the minimum number of vertices in a set S such that every vertex of the graph is either in S or adjacent to a member of S. The bondage number of a graph G is the cardinality of a smallest set of edges whose removal results in a graph with domination number greater than that of G. We prove that a graph with p vertices and bondage number b has at least p(b + 1)/4 edges, and for each b there is at least one p for which this bound is sharp. © 1999 Elsevier Science B.V. All rights reserve

Uniformly dissociated graphs

Creative Commons Attribution 3.0 International LicenseA set D of vertices in a graph G is called a dissociation set if every vertex in D has at most one neighbor in D. We call a graph G uniformly dissociated if all maximal dissociation sets are of the same cardinality. Characterizations of uniformly dissociated graphs with small cardinalities of dissociation sets are proven; in particular, the graphs in which all maximal dissociation sets are of cardinality 2 are the complete graphs on at least two vertices from which possibly a matching is removed, while the graphs in which all maximal dissociation sets are of cardinality 3 are the complements of the K4-free geodetic graphs with diameter 2. A general construction by which any graph can be embedded as an induced sub graph of a uniformly dissociated graph is also presented. In the main result we characterize uniformly dissociated graphs with girth at least 7 to be either isomorphic to C7, or obtainable from an arbitrary graph H with girth at least 7 by identifying each vertex of H with a leaf of a copy of P3

Exploiting eco-physiological niche to facilitate the separation of the freshwater cyanobacteria Microcystis sp. and Synechococcus sp.

In a novel approach to separate the co-occurring freshwater cyanobacteria Microcystis and Synechoccous, published ecological characteristics are used to manipulate temperature and nutrient concentrations to successfully establish a unialgal Microcystis strain. The simple protocol has implications for future cyanobacterial culturing approaches and the establishment of new cyanobacteria strains

Effect of Feeding Glyphosate-Tolerant (Roundup-Ready Events GA21 or nk603) Corn Compared with Reference Hybrids on Feedlot Steer Performance and Carcass Characteristics

Three experiments were conducted to compare the feeding value of genetically enhanced corn (Roundup Ready corn events GA21 and nk603) with nontransgenic hybrids. The four treatments included two separate reference hybrids (REF), the near-isogenic control hybrid (CON), and the genetically enhanced corn (RR), resulting in two preplanned comparisons of CON vs. RR and RR vs. the average of REF. In Exp. 1 (RR event GA21), 175 steers (BW = 427 kg) were fed in 25 pens with seven pens per corn hybrid, except CON, which contained four pens due to limited quantities of that hybrid. In Exp. 2 (RR event nk603), 196 steers (BW = &#;420 kg) were fed in 28 pens with seven pens per corn. In Exp. 3 (RR event nk603), 200 steers were fed in 20 pens, with a similar treatment design to Exp. 2 and five pens per corn. All experiments were conducted as completely randomized designs and utilized corn produced at University of Illinois (Exp. 1 and 2) and University of Nebraska (Exp. 3) research farms under identity-preserved protocols. In all experiments, DMI, ADG, and feed efficiency were similar (P \u3e 0.30) between RR and REF. In Exp. 1 and Exp. 2, RR was not different (P \u3e 0.25) than CON for growth performance. In Exp. 3, RR was not different from CON for ADG and DMI (P \u3e 0.15) or for feed efficiency (P = 0.08). No differences were observed between RR and CON or RR and REF for carcass weight, longissimus dorsi area, and marbling scores in any of the experiments. Subtle differences were observed between RR and either CON or REF for fat depth in each experiment; however, cattle fed RR were not consistently greater and varied from either the CON or the REF (but not both contrasts) within an experiment. Based on these results, insertion of glyphosate- tolerant genes had no significant effect on nutritive quality of corn. Performance and carcass characteristics were not influenced, which suggests that Roundup Ready corn is similar to conventional, nontransgenic corn when fed to finishing feedlot cattle

The effect of feeding modified soyabean oil enriched with C18 : 4 n-3 to broilers on the deposition of n-3 fatty acids in chicken meat

Supplementing broiler diets with conventional vegetable oils has little effect on the long-chain n-3 PUFA (LC n-3 PUFA) content of the meat. The present study investigated the effect on fatty acid composition and sensory characteristics of chicken meat when broilers were fed oil extracted from soyabeans (SDASOY) that had been genetically engineered to produce C18 : 4n-3 (stearidonic acid (SDA), 240 mg/g oil). Three diets were fed to 120 birds (eight replicate pens of five birds) from 15 d to slaughter (41–50 d). Diets were identical apart from the oil added to them (45 and 50 g/kg as fed in the grower and finisher phases, respectively), which was either SDASOY, near-isogenic soya (CON) or fish oil (FISH). The LC n-3 PUFA content of the meat increased in the order CON, SDASOY and FISH. In breast meat with skin, the SDA concentration was 522, 13 and 37 (sem 14·4) mg/100 g meat for SDASOY, CON and FISH, respectively. Equivalent values for C20 : 5n-3 (EPA) were 53, 13 and 140 (sem 8·4); for C22 : 5n-3 (docosapentaenoic acid (DPA)) 65, 15 and 101 (sem 3·5); for C22 : 6n-3 (DHA) 19, 9 and 181 (sem 4·4). Leg meat (with skin) values for SDA were 861, 23 and 68 (sem 30·1); for EPA 87, 9 and 258 (sem 7·5); for DPA 95, 20 and 165 (sem 5·0); for DHA 29, 10 and 278 (sem 8·4). Aroma, taste and aftertaste of freshly cooked breast meat were not affected. Fishy aromas, tastes and aftertastes were associated with LC n-3 PUFA content of the meat, being most noticeable in the FISH leg meat (both freshly cooked and reheated) and in the reheated SDASOY leg meat

Rainbow domination and related problems on some classes of perfect graphs

Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\gamma_{kr}(G)$ is the minimum of $\sum_{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs