Concepts of Graph Theory Relevant to Ad-hoc Networks

The issues in Mobile ad-hoc networks (MANETs) always bring the attention of research community. The fundamental issues of connectivity, scalability, routing and topol- ogy control in MANETS is worth to study. Graph theory plays an important role in the studyofthesefundamentalissues. Thispaperhighlightstheconceptsofgraphtheorythatare employed to address these fundamental issues.

[1]  Ivan Stojmenovic,et al.  Partial Delaunay triangulation and degree limited localized Bluetooth scatternet formation , 2004, IEEE Transactions on Parallel and Distributed Systems.

[2]  Christian Bettstetter,et al.  On the minimum node degree and connectivity of a wireless multihop network , 2002, MobiHoc '02.

[3]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[4]  Frank Harary,et al.  Graph Theory , 2016 .

[5]  Olle Häggström,et al.  Nearest Neighbor and Hard Sphere Models in Continuum Percolation , 1996 .

[6]  Lokanatha C. Reddy,et al.  A Study of Connectivity Index of Graph Relevant to Ad Hoc Networks , 2007 .

[7]  Mathew D. Penrose,et al.  Random Geometric Graphs , 2003 .

[8]  Ivan Stojmenovic,et al.  Routing with Guaranteed Delivery in Ad Hoc Wireless Networks , 2001, Wirel. Networks.

[9]  Yu-Chee Tseng,et al.  Increasing the throughput of multihop packet radio networks with power adjustment , 2001, Proceedings Tenth International Conference on Computer Communications and Networks (Cat. No.01EX495).

[10]  Roberto Tamassia,et al.  On-line maintenance of triconnected components with SPQR-trees , 1996, Algorithmica.

[11]  D. Cvetkovic,et al.  Spectra of Graphs: Theory and Applications , 1997 .

[12]  Asser N. Tantawi,et al.  Connectivity properties of a packet radio network model , 1989, IEEE Trans. Inf. Theory.

[13]  Charles E. Perkins,et al.  Ad Hoc Networking , 2001 .

[14]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.