The restricted edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This paper determines that the restricted edge-connectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the super edge-connectedness of B(d, n) is obtained immediately.

We survey results related to the data structures for dynamic graphs which can maintain global edge connectivity. We explain the major techniques used in these data structures and explore in detail the algorithm by Thorup for polylogarithmic edge-connectivity.

Motivated by challenges related to domination, connectivity, and information propagation in social and other networks, we initiate the study of the Vector Connectivity problem. This problem takes as input a graph G and an integer kv for every vertex v of G, and the objective is to find a vertex subset S of minimum cardinality such that every vertex v either belongs to S, or is connected to at l...

Brain connectivity network has been used for diagnosis and classification of neurodegenerative diseases, such as Alzheimer's disease (AD) as well as its early stage, i.e., mild cognitive impairment (MCI). However, conventional connectivity network is usually constructed based on the pairwise correlation among brain regions and thus ignores the higher-order relationship among them. Such informat...

The problem of enumerating connected induced subgraphs a given graph is classical and studied well. It known that can be enumerated in constant time for each subgraph. In this paper, we focus on highly subgraphs. most major concept connectivity graphs vertex connectivity. For connectivity, some enumeration settings algorithms have been proposed, such as k-vertex spanning another edge-connectivi...

Two important branches of graph connectivity problems are connectivity augmentation, which consists of augmenting a graph by adding new edges so as to meet a specified target connectivity, and connectivity orientation, where the goal is to find an orientation of an undirected or mixed graph that satisfies some specified edge-connection property. In the present work an attempt is made to link th...

In this paper we introduce a new compression technique for 2D vector fields which preserves the complete topology, i.e., the critical points and the connectivity of the separatrices. As the theoretical foundation of the algorithm, we show in a theorem that for local modifications of a vector field, it is possible to decide entirely by a local analysis whether or not the global topology is prese...

A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes up to 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerated and non-degenerated cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-de...

Conceptually graph vulnerability relates to the study of graphintactness when some of its elements are removed. The motivation forstudying vulnerability measures is derived from design and analysisof networks under hostile environment. Graph tenacity has been anactive area of research since the the concept was introduced in1992. The tenacity T(G) of a graph G is defined asbegin{center} $T(G)=di...