In this paper a data structure is presented to efficiently maintain the 2and 3-edge-connected components of a graph, under insertions of edges in the graph. Starting from an "empty" graph of n nodes, the insertion of e edges takes O( n log n + e) time in total. The data structure a.llows for insertions of nodes a.lso (in the same time bounds, taking n as the fina.l number of nodes). Moreover, a...

We find stability conditions ([D2], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the triangulated category is not naturally the derive...

‎the concept of the bipartite divisor graph for integer subsets has been considered in [‎m‎. ‎a‎. ‎iranmanesh and c‎. ‎e‎. ‎praeger‎, ‎bipartite divisor graphs for integer subsets‎, ‎{em graphs combin.}‎, ‎{bf 26} (2010) 95--105‎.]‎. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g...

the analysis of vulnerability in networks generally involves some questions about how the underlying graph is connected. one is naturally interested in studying the types of disruption in the network that maybe caused by failures of certain links or nodes. in terms of a graph, the concept of connectedness is used in dierent forms to study many of the measures of vulnerability. when certain ver...