Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes

The (1,2)-Step Competition Graph of a Tournament

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x,y}∈E(C1,2(D)) if and only if there exists a vertex z≠x,y, such that either dD−y(x,z)=1 and dD−x(y,z)≤2 or dD−x(y,z)=1 and dD−y(x,z)≤2. In this paper, we characterize the (1,2)-step competition graphs of tournaments and extend our results to the (i,k)-step competition graph of a tournament

Digraphs with Isomorphic Underlying and Domination Graphs: Pairs of Paths

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UGc (D) is the union of two disjoint paths

A Characterization of Connected (1,2)-Domination Graphs of Tournaments

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is an edge of G whenever x and y form a (1,2)-dominating pair in D. In this paper, we characterize all connected graphs that can be (I, 2)-dominating graphs of tournaments

Kings and Heirs: A Characterization of the (2,2)-domination Graphs of Tournaments

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom2,2(D). But of even more interest is that we are able to use the theorem to determine which other vertices, when paired with a king, form an edge in dom2,2(D). These vertices are referred to as heirs. Using kings and heirs, we are able to completely characterize the (2,2)-domination graphs of tournaments

Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided

Clinical review: Airway hygiene in the intensive care unit

Maintenance of airway secretion clearance, or airway hygiene, is important for the preservation of airway patency and the prevention of respiratory tract infection. Impaired airway clearance often prompts admission to the intensive care unit (ICU) and can be a cause and/or contributor to acute respiratory failure. Physical methods to augment airway clearance are often used in the ICU but few are substantiated by clinical data. This review focuses on the impact of oral hygiene, tracheal suctioning, bronchoscopy, mucus-controlling agents, and kinetic therapy on the incidence of hospital-acquired respiratory infections, length of stay in the hospital and the ICU, and mortality in critically ill patients. Available data are distilled into recommendations for the maintenance of airway hygiene in ICU patients

Characterization of digraphs with equal domination graphs and underlying graphs

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)] whenever (u,z)∈A(D) or (v,z)∈A(D) for every other vertex z∈V(D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given

Transitions of cardio-metabolic risk factors in the Americas between 1980 and 2014

Background: Describing the levels and trends of cardio-metabolic risk factors associated with non-communicable diseases (NCDs) is vital for monitoring progress, planning prevention and provide evidence to support policy efforts. We aimed to analyse the transition in body-mass index (BMI), obesity, blood pressure, raised blood pressure (RBP) and diabetes in the Americas, 1980-2014. Methods: Pooled analysis of population-based studies with data on anthropometric measurements, biomarkers for diabetes, and blood pressure from adults aged 18+ years. A Bayesian model was used to estimate trends in BMI, RBP (systolic blood pressure ≥140 mmHg or diastolic blood pressure ≥90 mmHg) and diabetes (fasting plasma glucose ≥7.0 mmol/l, history of diabetes, or diabetes treatment) from 1980 to 2014 in 37 countries and 6 sub-regions of the Americas. Findings: 389 population-based surveys from the Americas were available. Comparing the 2014 with the 1980 prevalence estimates, the obesity ratio was the largest in the non-English-speaking Caribbean sub-region (4.71 in men and 2.50 in women) showing that the prevalence in 2014 for men is almost five times larger than it was in 1980. The English-speaking Caribbean sub-region had the largest ratio regarding diabetes (2.14 in men and 2.13 in women). Conversely, the ratio for RBP signals that the frequency of this condition has diminished across the region; the largest decrease was found in North America (0.56 in men and 0.54 in women). Interpretation: Despite the generally high prevalence of cardio-metabolic risk factors across the Americas region, estimates also show a high level of heterogeneity in the transition between countries

Minimal dataset for post-registration surveillance of new drugs in hemophilia: communication from the SSC of the ISTH

Clinical epidemiolog