the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 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 $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

The problem of decomposition of a directed graph into its strongly connected components is a fundamental graph problem inherently present in many scientific and commercial applications. In this paper we show how existing parallel algorithms can be reformulated in order to be accelerated by NVIDIA CUDA technology. In particular, we design a new CUDA-aware procedure for pivot selection and we red...

The traditional, serial, algorithm for finding the strongly connected components in a graph is based on depth first search and has complexity which is linear in the size of the graph. Depth first search is difficult to parallelize, which creates a need for a different parallel algorithm for this problem. We describe the implementation of a recently proposed parallel algorithm that finds strongl...

The eeorts of the theory community to develop eecient PRAM algorithms often receive little attention from application programmers. Although there are PRAM algorithm implementations that perform reasonably on shared memory machines, they often perform poorly on distributed memory machines, where the cost of remote memory accesses is relatively high. We present a hybrid approach to solving the co...

In this paper, we calculate diameters of connected components of commuting graphs of GLn(S), for an integer n ≥ 2 and a commutative antinegative entire semiring S, unless n is a non-prime odd number and S has at least two invertible elements.

We calculate the connected components of the Gauge group of a Z/2 equivariant oriented 3-plane bundle and a related 4-plane bundle over the antipodal 3-sphere. This suggests that an obstruction which has earlier been claimed to vanish, does not necessarily do so.

The notion of “strength of connectedness” between pixels has been successfully used in image segmentation. We present extensions to these works, which can considerably improve the efficiency of object delineation tasks. A set of pixels is said to be a κ-connected component with respect to a seed pixel, when the strength of connectedness of any pixel in that set with respect to the seed is highe...

The main geometric objects of study in this paper are double Bruhat cells G = BuB∩B−vB− in a simply-connected connected complex semisimple group G; here B and B− are two opposite Borel subgroups in G, and u and v any two elements of the Weyl group W . Double Bruhat cells were introduced and studied in [5] as a geometric framework for the study of total positivity in semisimple groups; they are ...

The aim of this contribution is to find a way how to improve efficiency of current state-of-the-art satisfiability solvers. The idea is to split a given instance of the problem into parts (connected components) which can be solved separately. For this purpose we define component trees and a related problem of finding optimal component trees. We describe how this approach can be combined with st...

Frequently studied networks, such as social networks, are often massive, directed, and change over time. Thus studying network analysis algorithms in terms of data streaming is a practical model for understanding how companies and other organizations can process data in a useful, realistic way. One potentially interesting feature of a directed graph is strongly connected components. We design a...