On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

A survey on the set of periods of the graph homeomorphisms

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On algorithms for finding all circuits of a graph

Bibliography: p. [37]-[39]

Analysis of algorithms for finding all spanning trees of a graph.

"Supported in part by the following grants: US NSF GJ 217, US NSF GJ 812, and project BUILD."

The Eccentric Connectivity Polynomial of some Graph Operations

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Enterprise Collaboration Framework for Managing, Advancing and Unifying the Functionality of Multiple Cloud-Based Services with the Help of a Graph API

Part 5: Service Orientation in Collaborative Networks

Integration of a graph-based model indexer in commercial modelling tools

Softeam has over 20 years of experience providing UML-based modelling solutions, such as its Modelio modelling tool, and its Constellation enterprise model management and collaboration environment. Due to the increasing number and size of the models used by Softeam’s clients, Softeam joined the MONDO FP7 EU research project, which worked on solutions for these scalability challenges and produced the Hawk model indexer among other results. This paper presents the technical details and several case studies on the integration of Hawk into Softeam’s toolset. The first case study measured the performance of Hawk’s Modelio support using varying amounts of memory for the Neo4j backend. In another case study, Hawk was integrated into Constellation to provide scalable global querying of model repositories. Finally, the combination of Hawk and the Epsilon Generation Language was compared against Modelio for document generation: for the largest model, Hawk was two orders of magnitude faster.

SOME NEW INTEGRAL GRAPHS

The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph G is integral if all of its cigenvalues are integers. In this paper some new classes of integral graphs are constructed.

A recursive construction of the regular exceptional graphs with least eigenvalue -2

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Analyzing the effectiveness of graph metrics for anomaly detection in online social networks

Online social networks can be modelled as graphs; in this paper, we analyze the use of graph metrics for identifying users with anomalous relationships to other users. A framework is proposed for analyzing the effectiveness of various graph theoretic properties such as the number of neighbouring nodes and edges, betweenness centrality, and community cohesiveness in detecting anomalous users. Experimental results on real-world data collected from online social networks show that the majority of users typically have friends who are friends themselves, whereas anomalous users’ graphs typically do not follow this common rule. Empirical analysis also shows that the relationship between average betweenness centrality and edges identifies anomalies more accurately than other approaches.

Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.