On the odd girth and the circular chromatic number of generalized Petersen graphs

A class \(\mathcal{G}\) of simple graphs is said to be girth-closed (odd-girth-closed) if for any positive integer g there exists a graph \(\mathrm {G} \in \mathcal{G}\) such that the girth (odd-girth) of \(\mathrm {G}\) is \(\ge g\). A girth-closed (odd-girth-closed) class \(\mathcal{G}\) of graphs is said to be pentagonal (odd-pentagonal) if there exists a positive integer \(g^*\) depending on \(\mathcal{G}\) such that any graph \(\mathrm {G} \in \mathcal{G}\) whose girth (odd-girth) is greater than \(g^*\) admits a homomorphism to the five cycle (i.e. is \(\mathrm {C}_{_{5}}\)-colourable). Although, the question “Is the class of simple 3-regular graphs pentagonal?” proposed by Ne?et?il (Taiwan J Math 3:381–423, 1999) is still a central open problem, Gebleh (Theorems and computations in circular colourings of graphs, 2007) has shown that there exists an odd-girth-closed subclass of simple 3-regular graphs which is not odd-pentagonal. In this article, motivated by the conjecture that the class of generalized Petersen graphs is odd-pentagonal, we show that finding the odd girth of generalized Petersen graphs can be transformed to an integer programming problem, and using the combinatorial and number theoretic properties of this problem, we explicitly compute the odd girth of such graphs, showing that the class is odd-girth-closed. Also, we obtain upper and lower bounds for the circular chromatic number of these graphs, and as a consequence, we show that the subclass containing generalized Petersen graphs \(\mathrm {Pet}(n,k)\) for which either k is even, n is odd and \(n\mathop {\equiv }\limits ^{k-1}\pm 2\) or both n and k are odd and \(n\ge 5k\) is odd-pentagonal. This in particular shows the existence of nontrivial odd-pentagonal subclasses of 3-regular simple graphs.     

Religiosity,Citizenship and Belonging: The Everyday Experiences of Young Australian Muslims

Abstract

Since 11 September 2001 Muslim Diasporas have emerged as objects of anxiety in Western societies. Underlying this (in)security-driven problematisation is the question of whether Muslims living in the West have the capacity to become fully active citizens while maintaining their religious beliefs, rituals and practices. This apprehension has prompted reactionary government programmes, particularly targeting young Muslims. Such responses fail to recognise the societal capacities that practising Muslims possess, including those informed by the ethical precepts of Islamic faith. This paper argues that it is timely to explore expressions of Islamic religiosity as they are grounded in everyday multicultural environments. The paper draws on survey data and interviews conducted with Muslims living in Melbourne, Australia. We take into consideration key variables of age and generation to highlight how young, practising Muslims enact citizenship through Islamic rituals and faith-based practices and traditions. The paper will draw from key findings to argue that these performances provide a foundation for exploring ways of ‘living’ together in a manner that privileges ethics central to Islamic faith traditions.     

Organizational Factors Affecting Individuals to Donate to NPOs in the Turkish Context

VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations - While more and more people have been forced from their homes by natural disasters, wars, and violence, the citizens of the...     

Statistical analysis of rock-burst events in underground mines and excavations to present reasonable data-driven predictors

Rock bursts are sudden and violent failures of surrounding rockmasses in underground mines and excavations. In this paper, a database consisting of 188 case histories was collected. Each case history contains some of the predictor variables ‘overburden thickness, maximum tangential stress, uniaxial compressive strength of rock, tensile strength of rock, stress ratio, brittleness ratio and elastic energy index’ and one of the four defined classes for the dependent variable ‘rock burst intensity’. A strategy, including ‘outlier detection and substitution, normality evaluation, deduction of distribution functions, estimation of mean and mean variation ranges, evaluation of mean-equality and distribution function-equality hypotheses, correlation analysis and factor analysis for in-review variables’, was implemented. The strategy led to conclude that some predictor variables with available case histories have no contributions for rock burst prediction. These inferences were in accordance with the results of regression techniques for qualitative dependent variables. Besides, many predictor variable arrangements were incompatible with factor analysis. In the case of compatible arrangements, the variation of the predictor variables cannot be considerably reflected. Application of nonlinear principal component analysis using auto-associative neural networks did not also lead to representative components. Therefore, the significant predictor variables can only be used to design new classifiers.     

Race lines and spaces of political action among migrant youth

Recently proposed Anti-Racism Strategy established within a framework of the Australian Government's multicultural policy, People of Australia, identifies ‘youth engagement’ as one of the key areas that needs to be promoted and supported. Young people have been invited to join youth councils and youth forums and work with national, state and local policy-makers. Some have taken up this challenge and became public faces and active members of anti-racism campaigns. Others, however, either remained silent about the discrimination they face, or organised their own grassroots youth-based and youth-led initiatives. This paper discusses individual and collective responses to racism among young people in Australia, focusing on Melbourne, and examines possibilities in which racism, as a common experience among migrant youth, can be utilised to form alternative spaces for political action, challenging not only interpersonal, but also systemic forms of racism. By drawing attention towards institutional and systemic forms of racism, and the historical perpetuation of racist practices, these youth initiatives rely on legal measures, and argue that racism should be discussed in the context of the broader Australian society, not only in relation to minority groups.     

Structural Deficiency or Cultural Racism: The Educational and Social Experiences of Arab‐Australian Youth

This paper discusses the cultural, attitudinal and structural factors that impact upon the social experiences and educational achievements of Arabic‐speaking background (ASB) students in three Melbourne secondary schools with high levels of cultural and linguistic diversity. The paper makes the case for and then outlines a multidimensional approach to multicultural education to better integrate ASB students and their families into the schooling environment. Key strategies developed and tested include a model of school‐community partnership, online and interactive teacher support material (TSM) as well as on‐going teacher professional development workshops on reflexive approaches to cultural diversity and intercultural tension.     

B Butterfly Campaign: A social marketing campaign to promote normal childbirth among first-time pregnant women

Problem

The steep increase and inappropriateness of caesarean birth represent a healthcare problem in Iran.

Practices of active citizenship among migrant youth: beyond conventionalities

This paper discusses the empirical manifestations of the notion of active citizenship in the context of the experiences of migrant youth. It focuses on the practices of active citizenship through involvement in social networks and creative civic engagement. In doing so, the article examines the complex and multi-faceted nature of social networking among migrant youth and the extent to which their approach to engagement is dependent on the specificities of the local environment, the type of social issues involved, and the cultural norms of one's own cultural heritage. Key empirical insights are derived from quantitative and qualitative research conducted among migrant youth of African, Arabic-speaking and Pacific Island backgrounds in Australia. These empirical insights are used to examine the changing perceptions of active citizenship among migrant youth, and the possibilities offered through non-traditional networks to engender civic engagement and social participation.