Antimagic orientations of graphs with large maximum degree
DISCRETE MATHEMATICS
Authors: Yang, Donglei; Carlson, Joshua; Owens, Andrew; Perry, K. E.; Singgih, Inne; Song, Zi-Xia; Zhang, Fangfang; Zhang, Xiaohong
Abstract
Given a digraph D with m arcs, a bijection tau : A(D) -> {1, 2, ... , m} is an antimagic labeling of D if no two vertices in D have the same vertex-sum, where the vertex -sum of a vertex u in D under tau is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. We say (D, tau) is an antimagic orientation of a graph G if D is an orientation of G and tau is an antimagic labeling of D. Motivated by the conjecture of Hartsfield and Ringel (1990) on antimagic labelings of graphs, Hefetz et al. (2010) initiated the study of antimagic orientations of graphs, and conjectured that every connected graph admits an antimagic orientation. This conjecture seems hard, and few related results are known. However, it has been verified to be true for regular graphs and biregular bipartite graphs. In this paper, we prove that every connected graph G on n >= 9 vertices with maximum degree at least n - 5 admits an antimagic orientation. (c) 2020 Elsevier B.V. All rights reserved.
Effects of Pirfenidone and Nintedanib on Markers of Systemic Oxidative Stress and Inflammation in Patients with Idiopathic Pulmonary Fibrosis: A Preliminary Report
ANTIOXIDANTS
Authors: Fois, Alessandro G.; Sotgiu, Elisabetta; Scano, Valentina; Negri, Silvia; Mellino, Sabrina; Zinellu, Elisabetta; Pirina, Pietro; Pintus, Gianfranco; Carru, Ciriaco; Mangoni, Arduino A.; Zinellu, Angelo
Abstract
Introduction: In vitro evidence suggests that pirfenidone and nintedanib, approved agents for the treatment of idiopathic pulmonary fibrosis (IPF), exert anti-inflammatory and anti-oxidant effects. We aimed to investigate such effects in vivo in IPF patients. Methods: Systemic circulating markers of oxidative stress [nuclear factor erythroid 2-related factor 2 (Nrf2), thiobarbituric acid- reactive substances (TBARS), homocysteine (Hcy), cysteine (Cys), asymmetric dimethylarginine (ADMA) and ADMA/Arginine ratio, glutathione (GSH), plasma protein -SH (PSH), and taurine (Tau)] and inflammation [Kynurenine (Kyn), Tryptophan (Trp) and Kyn/Trp ratio] were measured at baseline and after 24-week treatment in 18 IPF patients (10 treated with pirfenidone and 8 with nintedanib) and in 18 age- and sex-matched healthy controls. Results: Compared to controls, IPF patients had significantly lower concentrations of reduced blood GSH (457 +/- 73 mu mol/L vs 880 +/- 212 mu mol/L, p < 0.001) and plasma PSH (4.24 +/- 0.95 mu mol/g prot vs 5.28 +/- 1.35 mu mol/g prot, p = 0.012). Pirfenidone treatment significantly decreased the Kyn/Trp ratio (0.030 +/- 0.011 baseline vs 0.025 +/- 0.010 post-treatment, p = 0.048) whilst nintedanib treatment significantly increased blood GSH (486 +/- 70 mu mol/L vs 723 +/- 194 mu mol/L, p = 0.006) and reduced ADMA concentrations (0.501 +/- 0.094 vs. 0.468 +/- 0.071 mu mol/L, p = 0.024). Conclusion: pirfenidone and nintedanib exert beneficial effects on specific markers of oxidative stress and inflammation in IPF patients.