L(j,k)- and circular L(j,k)-labellings for the products of complete graphs

Let j and k be two positive integers with j≥k. An L(j,k)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between labels of any two adjacent vertices is at least j, and the difference between labels of any two vertices that are at distance two apart is at least k. The minimum range of labels over all L(j,k)-labellings of a graph G is called the λ _j,k -number of G, denoted by λ _j,k (G). A σ(j,k)-circular labelling with span m of a graph G is a function f:V(G)→{0,1,…,m−1} such that |f(u)−f(v)| _m ≥j if u and v are adjacent; and |f(u)−f(v)| _m ≥k if u and v are at distance two apart, where |x| _m =min {|x|,m−|x|}. The minimum m such that there exists a σ(j,k)-circular labelling with span m for G is called the σ _j,k -number of G and denoted by σ _j,k (G). The λ _j,k -numbers of Cartesian products of two complete graphs were determined by Georges, Mauro and Stein ((2000) SIAM J Discret Math 14:28–35). This paper determines the λ _j,k -numbers of direct products of two complete graphs and the σ _j,k -numbers of direct products and Cartesian products of two complete graphs. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. This work is partially supported by FRG, Hong Kong Baptist University, Hong Kong; NSFC, China, grant 10171013; and Southeast University Science Foundation grant XJ0607230.     

Book reviews

Nurturing nature and the nature of science: Toward transcendence

As Nature Made Him: The Boy Who was Raised as a Girl. By John Colapinto. New York: HarperCollins, 2000, 288 pages. Cloth, $26.00.

The pedagogical value of as nature made him: The boy who was raised as a girl

As Nature Made Him: The Boy Who was Raised as a Girl. By John Colapinto. New York: HarperCollins, 2000, 288 pages. Cloth, $26.00.

What Americans Learned About Sex

Teaching America About Sex: Marriage Guides and Sex Manuals from the Late Victorians to Dr. Ruth. By M. E. Melody and Linda M. Peterson. New York: New York University Press, 1999, 304 pages. Cloth, $28.95.

Teen romance under the microscope

The Development of Romantic Relationships in Adolescence. Edited by Wyndol Furman, B. Bradford Brown, and Candice Feiring. New York: Cambridge University Press, 1999, 443 pages. Cloth, $49.95.

All hail the penis

Phallacies [Video]. Directed and produced by Vishnu Mathur. 2000. Available from Bullfrog Films, P. O. Box 149, Oley, PA 19547, www.bullfrogfilms.com. VHS, $250.     

Psychiatric Impact of Gender-Related Abuse Across the Life Course of Male-to-Female Transgender Persons

The psychiatric impact of interpersonal abuse associated with an atypical presentation of gender was examined across the life course of 571 male-to-female (MTF) transgender persons from the New York City Metropolitan Area. Gender-related abuse (psychological and physical), suicidality, and Diagnostic and Statistical Manual of Mental Disorders (4th ed., text revision) major depression were retrospectively measured across five stages of the life course using the Life Chart Interview. Among younger respondents (current age of 19–39), the impact of both types of abuse on major depression was extremely strong during adolescence and then markedly declined during later stages of life. Among older respondents (current age of 40–59), the impact of both types of abuse on major depression was strong during adolescence and then marginally declined during later stages of life. The effects of both types of abuse on suicidality were weaker but more consistently observed across the life course among both the younger and older respondents. Gender-related abuse is a major mental health problem among MTF transgender persons, particularly during adolescence. As these individuals mature, however, the consequences of this abuse appear less severe, which may represent the development of moderately effective mechanisms for coping with this abuse.     

The Portuguese Republic

The findings and recommendations of researchers and specialists in thinking-skill learning and teaching have important implications for classroom efforts to improve student thinking. This summary identifies various types of thinking skills and skill components recommended for classroom instruction. The author describes and cites research-derived features of effective, direct instruction in thinking skills and describes a framework for this instruction. He also describes researcherand specialist-recommended teaching techniques and lesson strategies for introducing any thinking skill, guiding continuing skill practice, and teaching students to transfer thinking skills to other contexts. He presents researcher recommendations of when, where, and why such direct skill instruction can be effectively provided. The research cited here suggests both students' academic achievement and their quality of thinking can be improved by using these techniques and strategies to teach thinking skills in subject-matter courses.     

Multi-profile intergenerational social choice

In an infinite-horizon setting, Ferejohn and Page showed that any social welfare function satisfying Arrow’s axioms and stationarity must be a dictatorship of the first generation. Packel strengthened this result by proving that no collective choice rule generating complete social preferences can satisfy unlimited domain, weak Pareto and stationarity. We prove that this impossibility survives under a domain restriction and without completeness. We propose an alternative stationarity axiom and show that a social welfare function on a specific domain satisfies this modified version and some standard social choice axioms if and only if it is a chronological dictatorship.     

Humanitarian work psychology: The contributions of organizational psychology to poverty reduction

Achieving the MDG goal of reducing world poverty by 50% by 2015 requires the cooperative effort of many disciplines. To date the discipline of organizational psychology has not played as significant a role as it might in this endeavor. With the recent establishment of the Global Task Force for Humanitarian Work Psychology, this discipline signaled its commitment to the global effort. Organizational psychology offers to bring its expertise to poverty reduction: its ability to assess needs and capacity, develop partnerships with stakeholders, bring about and manage change, and systematically review, evaluate, monitor and revise high level mandates, policy development, program implementation and consultation on personnel issues. Its successes as practitioners-scientists in private enterprise will enhance its credibility for success in the public sphere. The article reviews the research and practice of some of the organizational psychologists presently engaged in poverty reduction and how humanitarian work psychology might enhance the efforts of anti-poverty organizations.     

Multicultural supervision: lessons learned about an ongoing struggle

This article examines the experiences of seven diverse therapists in a supervision course as they wrestled with the real-world application of multicultural supervision. Existing literature on multicultural supervision does not address the difficulties that arise in addressing multicultural issues in the context of the supervision relationship. The experiences of six supervisory candidates and one mentoring supervisor in addressing multicultural issues in supervision are explored. Guidelines for conversations regarding multicultural issues are provided.     

Diversity,Disruption, Continuity: Parenting and Social and Emotional Wellbeing Amongst Aboriginal Peoples and Torres Strait Islanders

This paper reviews the diversity in parenting values and practices amongst Aboriginal peoples and Torres Strait Islanders. First, issues arising from the historical traumatic disruption of families' attachments are discussed. Then the contribution Indigenous parenting makes to the development of healthy and vulnerable individuals becomes the central focus. Family therapists can draw from a broad understanding of the diversity of parenting values and practices in the context of a strength‐based approach.