The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.

Preface Graphs are often used as a model for networks, for example transport networks, telecommunication systems, a network of servers and so on. Typically, the networks and thus the representing graphs are connected; that means, that there exists a path between all pairs of two vertices in the graph. But sometimes an element of the network fails, for the graphs that means the removal of a vert...

Given an undirected graph G and vertices s, t ∈ V (G), the undirected connectivity problem is to decide whether there is a path from s to t in G. If G has N vertices and M edges, then the existence of a path between s and t implies the existence of a path of length at most N . If A is the adjacency matrix of G and G has, without loss of generality, self-loops on every vertex, then s and t are c...

In this thesis we are concerned with the solution-space structure of Boolean satisfiability problems, from the view of theoretical computer science, especially complexity theory. We consider the solution graph of Boolean formulas; this is the graph where the vertices are the solutions of the formula, and two solutions are connected iff they differ in the assignment of exactly one variable. For ...

Background: Early diagnosis of patients in the early stages of Alzheimer's, known as mild cognitive impairment, is of great importance in the treatment of this disease. If a patient can be diagnosed at this stage, it is possible to treat or delay Alzheimer's disease. Resting-state functional magnetic resonance imaging (fMRI) is very common in the process of diagnosing Alzheimer's disease. In th...

let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

Previous studies suggest that spontaneous fluctuations in the resting-state fMRI (RS-fMRI) signal may reflect fluctuations in transverse relaxation time (T(2)(*)) rather than spin density (S(0)). However, such S(0) and T(2)(*) features have not been well characterized. In this study, spatial and spectral characteristics of functional connectivity on sensorimotor, default-mode, dorsal attention,...

if we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.in this paper we discuss...

On Approximate Min-Max Theorems for Graph Connectivity Problems Lap Chi Lau Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2006 Given an undirected graph G and a subset of vertices S ⊆ V (G), we call the vertices in S the terminal vertices and the vertices in V (G) − S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high...

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. A finite number of buffered n...