In Source Location (SL) problems the goal is to select a minimum cost source set S such that the connectivity from S to any node v is at least the demand dv of v. In Network Augmentation (NA) problems we are given a graph G = (V,E) and an edge-set F on V , edge-costs on F or node-costs on V , and connectivity requirements {rsv : sv ∈ D} on a set D of “demand edges”. The goal is to compute a min...

A vertex-cut S is called a super if G − disconnected and it contains no isolated vertices. The super-connectivity , κ ′, the minimum cardinality over all vertex-cuts. This article provides bounds for connectivity of direct product an arbitrary graph complete K n . Among other results, we show that non-complete with girth( ) = 3 ′( ∞, then × ≤ min{ mn 6, m ( 1) + 5, 5 8}, where | V )|

Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number ` of edge-disjoint trees T1, T2, . . . , T` in G such that V (Ti) ∩ V (Tj) = S for every pair of distinct integers i, j with 1 ≤ i, j ≤ `. Chartrand et al. generalized the concept of connectivity as follows: The kconnectivity of G, denoted by κk(G...

An exciting application of Multi-hop Packet Radio Networks (MPRNet) is to provide communication services in environments without suitable infrastructure. One key design issue in MPRNet is the formulation of Medium Access Control (MAC) protocols. In this paper, the performance of two MAC protocols, Slotted ALOHA (S-ALOHA) and Spatial TDMA (S-TDMA), are investigated. In many MPRNet, the traffic l...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. a failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. a number of approaches have bee...

Directed st-connectivity is the problem of detecting whether there is a path from a distinguished vertex s to a distinguished vertex t in a directed graph. We prove time–space lower bounds of ST = Ω( n 2 log n log(n log n/S) ) and S 1

Abstract Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining visualization. However, existing often fail preserve connectivity important structures original graph. This paper introduces a new divide conquer approach spectral based on connectivity, called BC Tree (i.e., decomposition connected into biconnected components) sparsificatio...

Resting-state studies conducted with stroke patients are scarce. The study of brain activity and connectivity at rest provides a unique opportunity for the investigation of brain rewiring after stroke and plasticity changes. This study sought to identify dynamic changes in the functional organization of the default mode network (DMN) of stroke patients at three months after stroke. Eleven patie...

The concept of pendant tree-connectivity was introduced by Hager in 1985. For a graph G = (V,E) and a set S ⊆ V (G) of at least two vertices, an S-Steiner tree or a Steiner tree connecting S (or simply, an S-tree) is a subgraph T = (V ′, E ′) of G that is a tree with S ⊆ V ′. For an S-Steiner tree, if the degree of each vertex in S is equal to one, then this tree is called a pendant S-Steiner t...