The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. In this paper, we present new upper bounds for b(G) in terms of girth, order and Euler characteristic.

The bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number (G) ofG. Kang andYuan proved b(G) 8 for every connected planar graph G. Fischermann, Rautenbach and Volkmann obtained some further results for connected planar graphs. In this paper, we generalize their results ...

the first aim of this article is to present zahed’s conceptual–operational model of freedom on the basis of islamic thoughts.  the second goal is to distinguish how freedom would run in the islamic society according to this operational model. finally, we will talk about the differences between this new conceptualization of freedom and the secular one. we will introduce theoretical, social and c...