Untitled

Grigoriev, Alexander; Loon, Joyce van; Sitters, René; Uetz, Marc

doi:10.1002/net.v53:1

Cited by 10 publications

References 190 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Introduction to Random Graphs

2015

View full text Add to dashboard Cite

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

show abstract

Introduction to Random Graphs

2015

View full text Add to dashboard Cite

show abstract

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Calamoneri

2011

The Computer Journal

160

104

View full text Add to dashboard Cite

Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.

show abstract

Connectivity in secure wireless sensor networks under transmission constraints

Zhao

Yağan

Gligor

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although the connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real-world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present the first zero-one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws improve recent results [10, 11] significantly, are sharp, and help specify the critical transmission ranges for connectivity. Our analytical findings, which are also confirmed via numerical experiments, provide precise guidelines for the design of secure WSNs in practice. The application of our theoretical results to frequency hopping of wireless networks is discussed in some detail.

show abstract

Untitled

Cited by 10 publications

References 190 publications

Introduction to Random Graphs

Introduction to Random Graphs

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Connectivity in secure wireless sensor networks under transmission constraints

Contact Info

Product

Resources

About