The bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smallest set E of edges of G such that the graph G − E has domination number greater than that of G. In this paper we present a simplified proof that b(G) ≤ min{8,∆(G) + 2} for all planar graphs G, give examples of planar graphs with bondage number 6, and bound the bondage number of directed graphs.

Despite recent multilateral efforts to single out child labor in debt bondage as one of the worst forms of child labor, several important questions have yet to be addressed: Howpervasive is the phenomenon?Are there systematic correlations between the incidence of children in debt bondage and the economic, legislative, and financial development indicators of the economy? How does an understandin...

This paper focuses on the comparison between Augustine’s and Luther’s understanding of bondage will. As a philosopher will, Augustine establishes independence will in his earlier work. In debate with Julian Eclanum that comes from later period, emphasizes grace original sin. The salvation freedom humans rely Holy Spirit. Erasmus, Luther introduced conception necessity However, both thinkers hav...

Let G = (V,E) be a graph. A subset D ⊆ V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a n...

Let G = (V , E) be a graph. A subset D ⊆ V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a...

Autoerotic asphyxia is the practice of self-inducing cerebral anoxia, usually by hanging, strangulation, or suffocation, during masturbation. This study investigated the relationships between: asphyxiators' ages; two paraphilias commonly accompanying autoerotic asphyxia, bondage and transvestism; and various other types of simultaneous sexual behaviour. Subjects were two concurrent series total...

For a graphical property P and a graph G, a subset S of vertices of G is a P-set if the subgraph induced by S has the property P . The domination number with respect to the property P , denoted by γP(G), is the minimum cardinality of a dominating P-set. The bondage number with respect to the property P of a nonempty graph G, denoted bP(G), is the cardinality of a smallest set of edges whose rem...