Ugly Duckling to Swan: Labeling Theory and the Stigmatization of Red Hair

Interviews were conducted with redheads, and labeling theory is used to analyze their stigmatization in society as well as their perceptions of having red hair. First, using the relativistic stance of labeling theory, red hair is described as a type of deviance. Second, the processes involved in the labeling of redheads are examined, especially in regard to how redheads have personally experienced stereotyping. The stereotypes that redheads perceive to be socially constructed are as follows: hot temper, clownish, weirdness, Irishness, not capable of being in the sun, wild women, wimpy men, and intellectual superiority. Finally, the impact of being negatively labeled and treated in society is considered. Redheads typically receive negative treatment as children, and, as a consequence, redheads experience a lowered self-esteem, feelings of differentness, and a sense of being the center of attention. Nevertheless, redheads typically transform a negative experience into a positive one by learning to appreciate their hair color and how it has shaped their sense of self. In essence, they become an example of tertiary deviants.     

Which trees have a differentiating-paired dominating set?

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. The set S is called a differentiating-paired dominating set if for every pair of distinct vertices u and v in V(G), N[u]∩S≠N[v]∩S, where N[u] denotes the set consisting of u and all vertices adjacent to u. In this paper, we provide a constructive characterization of trees that do not have a differentiating-paired dominating set.     

Paired versus double domination in K 1,r -free graphs

A vertex in G is said to dominate itself and its neighbors. A subset S of vertices is a dominating set if S dominates every vertex of G. A paired-dominating set is a dominating set whose induced subgraph contains a perfect matching. The paired-domination number of a graph G, denoted by γ _pr(G), is the minimum cardinality of a paired-dominating set in G. A subset S?V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ _×2(G). A claw-free graph is a graph that does not contain K _1,3 as an induced subgraph. Chellali and Haynes (Util. Math. 67:161–171, 2005) showed that for every claw-free graph G, we have γ _pr(G)≤γ _×2(G). In this paper we extend this result by showing that for r≥2, if G is a connected graph that does not contain K _1,r as an induced subgraph, then $\gamma_{\mathrm{pr}}(G)\le ( \frac{2r^{2}-6r+6}{r(r-1)} )\gamma_{\times2}(G)$ .     

k-tuple total domination in cross products of graphs

For k??1 an integer, a set S of vertices in a graph G with minimum degree at least?k is a k-tuple total dominating set of G if every vertex of G is adjacent to at least k vertices in S. The minimum cardinality of a k-tuple total dominating set of G is the k-tuple total domination number of G. When k=1, the k-tuple total domination number is the well-studied total domination number. In this paper, we establish upper and lower bounds on the k-tuple total domination number of the cross product graph G×H for any two graphs G and H with minimum degree at least?k. In particular, we determine the exact value of the k-tuple total domination number of the cross product of two complete graphs.     

Independent domination in subcubic graphs

Journal of Combinatorial Optimization - A set S of vertices in a graph G is a dominating set if every vertex not in S is adjacent to a vertex in S. If, in addition, S is an independent...