Is there any polynomial upper bound for the universal labeling of graphs?

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem.     

Operational Slack and Venture Survival

Slack can act as a double‐edged sword. While it can buffer against environmental threats to help ensure business continuity, slack can also be costly and reduce profitability. In this study we focus on operational slack, the form related to the firm's production processes. We investigate the role of operational slack on firm survival during its venture stage when its survival is significantly challenged by environmental threats. Specifically, we explore how change in three types of environmental uncertainty, namely dynamism, complexity, and lack of munificence, affect the relationship between operational slack and venture survival. Results suggest that with an increase in environmental uncertainty, operational slack lowers the likelihood of venture failure.     

The association between social support and postpartum depression in women: A cross sectional study

Background

Prevalence of postpartum depression is estimated to be about 10–15% worldwide. Many risk factors are supposed to play a role leading a new mother to maternal postpartum depression which can considerably affect the baby, mother, family and also the society.

An integrated response to trauma in three post office businesses

Abstract

This paper looks at the way the UK Post Office has developed a core trauma care programme that is capable of being adapted to meet the needs of three of its businesses. The core programme includes an introductory stage that is involved in the selection and education of the workforce and the promotion of the programme; crisis management; manager debriefing; psychological debriefing; trauma counselling; and a final stage involving the evaluation of the programme and following up traumatized employees. The core programme was tailored to the needs of each of the three Post Office businesses, using information on the business operation, culture and policies of the businesses in the light of the nature and range of the traumatic incidents that affect their workforce.     

Shortest paths among transient obstacles

Journal of Combinatorial Optimization - We present an optimal algorithm for determining a time-minimal rectilinear path among transient rectilinear obstacles. An obstacle is transient if it exists...     

Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

We propose data generating structures which can be represented as a mixture of autoregressive-autoregressive conditionally heteroscedastic models. The switching between the states is governed by a hidden Markov chain. We investigate semi-parametric estimators for estimating the functions based on the quasi-maximum likelihood approach and provide sufficient conditions for geometric ergodicity of the process. We also present an expectation–maximization algorithm for calculating the estimates numerically.     

The Socioeconomic Status of Street Children in Iran: A Systematic Review on Studies over a Recent Decade

To document the socioeconomic situation of street children in Iran and to ascertain the part played by this in becoming a street child, we classified and evaluated studies on this issue from the recent decade according to their strengths and weaknesses. The results will be helpful in policy‐making and planning for this group. The study employed a systematic review methodology, searching Iranian and international databases, and many universities and related organisations in Iran. After the quality of studies had been evaluated by three researchers, the findings of 40 research studies were classified, described and analysed. The research finds that street children in Iran come from crowded, low‐income families; many of them were rural–urban migrants and Afghans with families who immigrated to Iran; most of their parents had a lower than high school education and many of their fathers were unemployed or had low‐income jobs; the majority of these children were unskilled workers who would work many hours of the day for negligible incomes. We conclude that low socioeconomic status was prevalent among the street children's families in Iran and seems to be an important factor in the street‐connectedness of the children.     

Quality of life and sexual function in postmenopausal women

This study examined the relationship between quality of life (QoL) and sexual function among postmenopausal women. As a cross-sectional study, it was conducted among 405 postmenopausal women selected using a multistage sampling method. The data-collection tools were the Female Sexual Function Index (FSFI) questionnaire, the WHO Quality of Life-BREF (WHOQOL-BREF) questionnaire, and a researcher-administered questionnaire. Sexual dysfunction was observed in 61% of the participants. The total scores of FSFI had a positive correlation with the WHOQOL-BREF total scores and all QoL domain scores. Therefore, sexual function needs to be covered by health-care packages aiming to improve postmenopausal women’s QoL.     

The Effects of Strategic and Structural Supply Chain Orientation on Operational and Customer‐Focused Performance

Supply chain orientation (SCO), or the implementation of a supply chain management philosophy, consists of two distinct, yet interdependent elements, namely strategic SCO and structural SCO. Strategic SCO involves integrating an SCM philosophy into the firm's strategy development, while structural SCO encompasses operational‐level behaviors and actions that reflect such a philosophy. This study extends the research on SCO by developing hypotheses on the contingent effects of strategic SCO and structural SCO on a firm's operational and customer‐focused performance. Drawing on the strategy‐structure‐performance framework, the study proposes that strategic SCO and structural SCO positively affect different dimensions of performance and that structural SCO plays a mediating role in the relationship between strategic SCO and performance. These relationships are tested using primary survey data and archival data from 183 manufacturers in the Midwestern US. Results confirm that strategic SCO is associated with both operational performance and customer‐focused performance, but structural SCO is only related to operational performance. Structural SCO acts as a mediator in linking strategic SCO with operational performance and customer‐focused performance and mediation effects are strengthened at higher levels of environmental dynamism.