Paired-domination in inflated graphs

2003-2004 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Total domination in inflated graphs

AbstractThe inflation GI of a graph G is obtained from G by replacing every vertex x of degree d(x) by a clique X=Kd(x) and each edge xy by an edge between two vertices of the corresponding cliques X and Y of GI in such a way that the edges of GI which come from the edges of G form a matching of GI. A set S of vertices in a graph G is a total dominating set, abbreviated TDS, of G if every vertex of G is adjacent to a vertex in S. The minimum cardinality of a TDS of G is the total domination number γt(G) of G. In this paper, we investigate total domination in inflated graphs. We provide an upper bound on the total domination number of an inflated graph in terms of its order and matching number. We show that if G is a connected graph of order n≥2, then γt(GI)≥2n/3, and we characterize the graphs achieving equality in this bound. Further, if we restrict the minimum degree of G to be at least 2, then we show that γt(GI)≥n, with equality if and only if G has a perfect matching. If we increase the minimum degree requirement of G to be at least 3, then we show γt(GI)≥n, with equality if and only if every minimum TDS of GI is a perfect total dominating set of GI, where a perfect total dominating set is a TDS with the property that every vertex is adjacent to precisely one vertex of the set

A polynomial-time algorithm for the paired-domination problem on permutation graphs

Author name used in this publication: T. C. E. Cheng2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Distance paired-domination problems on subclasses of chordal graphs

AbstractLet G=(V,E) be a graph without isolated vertices. For a positive integer k, a set S⊆V is a k-distance paired-dominating set if each vertex in V−S is within distance k of a vertex in S and the subgraph induced by S contains a perfect matching. In this paper, we present two linear time algorithms to find a minimum cardinality k-distance paired-dominating set in interval graphs and block graphs, which are two subclasses of chordal graphs. In addition, we present a characterization of trees with unique minimum k-distance paired-dominating set

Vigilantism, Current Racial Threat, and Death Sentences

Capital punishment is the most severe punishment, yet little is known about the social conditions that lead to death sentences. Racial threat explanations imply that this sanction will be imposed more often in jurisdictions with larger minority populations, but some scholars suggest that a tradition of vigilante violence leads to increased death sentences. This study tests the combined explanatory power of both accounts by assessing statistical interactions between past lynchings and the recent percentage of African Americans after political conditions and other plausible effects are held constant. Findings from count models based on different samples, data, and estimators suggest that racial threat and lynchings combine to produce increased death sentences, but the presence of liberal political values explains the absence of death sentences. These findings both confirm and refine the political version of conflict theory because they suggest that the effects of current racial threat and past vigilantism largely directed against newly freed slaves jointly contribute to current lethal but legal reactions to racial threat