Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Evaluation of Electro Physiological Changes of Sleep among Patients with Supratentorial Ischemic Stroke and Comparison with Control group

Abstract: Background & Aims: Sleep disorders are common complains in patients with cerebral stroke; studies on these issues are limited. We aimed to evaluate the sleep changes in patients with supratentorial ischemic stroke. Methods: In this cross sectional study, 38 patients (19 patients in supratentorial ischemic stroke group and 19 people in control group) were evaluated. Total sleep time, sleep efficacy, percent of stage 2 of Non-rapid eye movement (NREM) sleep, Rapid eye movement (REM) latency, sleep spindle, sleep intensity, and saw tooth wave were evaluated by Electroencephalogram (EEG) monitoring during sleep in both groups and were compared between them. Results: Patients in supratentorial ischemic stroke group had less sleep efficacy (P < 0.01), shorter stage 2 of NREM sleep (P < 0.01), greater REM latency (P < 0.05) and lesser sleep spindles (P < 0.01) in comparison with those in control group. There was no significant difference in saw tooth wave between two groups. Significant differences observed between two hemisphere in sleep density (P = 0.01) and REM latency (P < 0.05). Conclusion: Supratentorial ischemic stroke accompanied with sleep changes on EEG monitoring. These changes were seen in both REM and NREM periods and showed that supratentorial structures are involved in sleep–awake process. Keywords: Supratentorial ischemic stroke, Electroencephalogram monitoring, Slee

Comparison of the importance and observance of the patient's bill of rights from the perspectives of patients and personnel of hospitals in Kerman

Patients� rights are among the most important criteria for evaluating the quality of health services. The current study aimed to determine the importance and observance of the patient's bill of rights. This cross-sectional study was done in Kerman, Iran. The research samples were 217 patients and 204 personnel. The data collection tool was a researcher-made questionnaire in the scope of the patient's bill of rights, and data were analyzed by SPSS 15. The results showed a significant difference between patients and the personnel on the subject of the patient's bill of rights and most of its dimensions (P < 0.01). However, no significant difference was found between their views on the observance of the patient's bill of rights and its dimensions. Also, 35.9 of patients as well as 25 of personnel considered the observance of patients� rights unfavorable. The participants were aware of the importance of the patient's bill of rights. It is necessary, however, to codify and approve the laws related to the rights of patients. © 2020 Medical Ethics and History of Medicine Research Center, Tehran University of Medical Sciences. All rights reserved

Stress and Quality of Life of Patients with Cancer: The Mediating Role of Mindfulness

Background. Cancer is one of the major health problems worldwide, which in addition to physical disorders, causes stress and anxiety in patients and affects the quality of life of cancer patients. Mindfulness can affect stress and improve the quality of life. This research explained the correlation between stress, quality of life, and mindfulness. Materials and Methods. Two hundred five cancer patients participated in this cross-sectional study. Patients completed the EORTC Quality of Life Questionnaire Core 30 (EORTC QLQ-C30), the Mindfulness Attention and Awareness Scale (MAAS), and Perceived Stress Scale (PSS). Results. Perceived stress and mindfulness predict nearly 39 of the changes of QOL in cancer patients. In addition, perceived stress was negatively associated with mindfulness and quality of life P<0.05. Mindfulness was positively correlated with quality of life P<0.05. Mindfulness played a mediating role in the relationship between perceived stress and quality of life (standardized β =-0.13; SE = 0.07, 95 confidence interval =-0.28 to-0.01; P value = 0.04). Conclusion. In the present study, the variables of mindfulness and perceived stress affected the quality of life of cancer patients. Mindfulness can affect the quality of life of cancer patients directly and indirectly. These results emphasize the importance of mindfulness in the lives of cancer patients. © 2020 Mahlagha Dehghan et al