BACKGROUND AND AIM COPD is a progressive and irreversible disease, thus assessing the impact of the disease on health-related quality of life (HRQOL) is important in the management of COPD. The aim of this study was to examine the relationship between HRQOL, lung function and dyspnea rating in patients with stable COPD. METHODS One hundred COPD patients (mean age = 64.76 +/- 11.43 years) were...

Let G = (V,E) be a graph. A k-coloring of a graph G is a labeling f : V (G) → T , where | T |= k and it is proper if the adjacent vertices have different labels. A graph is k-colorable if it has a proper k-coloring. The chromatic number χ(G) is the least k such that G is k-colorable. Here we study chromatic numbers in some kinds of Harary graphs. Mathematics Subject Classification: 05C15

The metric dimension problem was first introduced in 1975 by Slater [12], and independently by Harary and Melter [6] in 1976; however the problem for hypercube was studied (and solved asymptotically) much earlier in 1963 by Erdős and Rényi [4]. A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G...

This study reports the use of multicenter bond indices as a new tool for the quantitative characterization of homoaromaticity. The approach was applied to the series bicyclic systems whose homoaromaticity was recently discussed in terms of traditional aromaticity index, namely, NICS. In this study we found that the multicenter bond indices are indeed able to quantify the degree of homoaromatici...

J. A. Bondy and U. S. R. Murty, Graph theory with Applications, London: MacMillan (1976). R. M. Gera, On Dominator Colorings in Graphs, Graph Theory Notes of New York LIT, 25-30 (2007) F. Harary, Graph Theory, Narosa Publishing 1969. D. Michalak, On Middle and Total graphs with Coarseness Number Equal 1, Lecture Notes in Mathematics, Volume 1018: Graph Theory, Springer-Verlag, Berlin, 139 – 150...

The Harary-Hill conjecture states that the minimum number of crossings in a drawing of the complete graph Kn is Z(n) := 1 4 ⌊ n 2 ⌋ ⌊ n−1 2 ⌋ ⌊ n−2 2 ⌋ ⌊ n−3 2 ⌋ . This conjecture was recently proved for 2-page book drawings of Kn. As an extension of this technique, we prove the conjecture for monotone drawings of Kn, that is, drawings where all vertices have different x-coordinates and the edg...

Methods A multicenter prospective cohort study was conducted with all consecutive adult patients admitted to mixed medical-surgical ICUs in Southern Brazil between May 2014 and December 2014. The decline of functional status in the period ranging from 3 months before ICU admission to 3 months after ICU discharge was evaluated through variations in Barthel index score. A stepwise multiple linear...

Sonlu bir Z_n grubunun yönlendirilmemiş P(Z_n ) power grafı, köşelerinin kümesi olan bağlantılı graftır ve burada iki köşe komşudur gerek yeter şart u≠v ⊆ veya dir. 〖(Z〗_n,+) grubuna karşılık gelen Yönlendirilmemiş G=P(Z_n grafının Hyper-Wiener, SK, 〖SK〗_1, 〖SK〗_2 Harary indeksleri sırasıyla, 1/2 ∑_({u,v}⊆V(G))▒〖d(u,v)〗+1/2 ∑_({u,v}⊆V(G))▒〖d^2 (u,v) 〗 ∑_(uv∈E(G))▒〖d(u)+d(v)〗, ∑_(uv∈E(G))▒〖d(u)....

and Dedication This paper is an exploration of simple four-regular graphs in the plane (i.e. loopless and with no more than one edge between any two nodes). Such graphs are fundamental to the theory of knots and links in three dimensional space, and their planar diagrams. We dedicate this paper to Frank Harary (1921 – 2005) whose fascination with graphs of knots inspired this work and with whom...