She is the chair(man): Gender,language, and leadership

This article presents results from two complementary experiments that examine the effects of a potential obstacle to female leadership: gendered language in the form of masculine leadership titles. In the first experiment (N = 1753), we utilize an unobtrusive writing task to find that a masculine title (“Chairman” vs. “Chair”) increases assumptions that a hypothetical leader is a man, even when the leader’s gender is left unspecified. In the second experiment (N = 1000), we use a surprise recall task and a treatment that unambiguously communicates the leader’s gender to find that a masculine title increases the accuracy of leader recollection only when the leader is a man. In both studies, we find no significant differences by gender of respondents in the effects of masculine language on reinforcing the link between masculinity and leadership. Thus, implicitly sexist language as codified in masculine titles can reinforce stereotypes that tie masculinity to leadership and consequently, weaken the connection between women and leadership.     

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.