CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
Reseach Article

Clique Matrix of a Graph in Traffic Control Problems

by Arun Kumar Baruah, Niky Baruah
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 53 - Number 6
Year of Publication: 2012
Authors: Arun Kumar Baruah, Niky Baruah
10.5120/8427-2194

Arun Kumar Baruah, Niky Baruah . Clique Matrix of a Graph in Traffic Control Problems. International Journal of Computer Applications. 53, 6 ( September 2012), 41-45. DOI=10.5120/8427-2194

@article{ 10.5120/8427-2194,
author = { Arun Kumar Baruah, Niky Baruah },
title = { Clique Matrix of a Graph in Traffic Control Problems },
journal = { International Journal of Computer Applications },
issue_date = { September 2012 },
volume = { 53 },
number = { 6 },
month = { September },
year = { 2012 },
issn = { 0975-8887 },
pages = { 41-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume53/number6/8427-2194/ },
doi = { 10.5120/8427-2194 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:53:26.576919+05:30
%A Arun Kumar Baruah
%A Niky Baruah
%T Clique Matrix of a Graph in Traffic Control Problems
%J International Journal of Computer Applications
%@ 0975-8887
%V 53
%N 6
%P 41-45
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Clique matrix can be used as a graph theoretic tool to study traffic control problem at an intersection. A traffic control problem can be efficiently modelled as a graph where the nodes represent the traffic streams and the edges represent the relationship among the streams. The matrix representation of the control problem is used for phasing of signal groups and thus providing a solution to the control problem. Clique of a graph is defined as maximal complete subgraph and clique matrix of a graph is defined as a generalization of the incidence matrix where the columns correspond to the number of cliques and the rows correspond to the number of vertices of the graph.

References
  1. Gazis, D. C. , 1970, Traffic Science, John Wiley & Sons, New York.
  2. Gazis, D. C. , 2002, Traffic Theory, Kluwer Academic Publishers, London.
  3. Guberinic, S. , Senborn, G. , Lazic, B. , 2008, Optimal Traffic Control : Urban Intersection, CRC Press.
  4. Review of Road Traffic Control Strategies : Proceeding of the IEEE, Vol. 91, No. 12, December 2003.
  5. Barber, D. , 2008, Clique Matrices for Statistical Graph Decomposition and Parameterising Restricted Positive Definite Matrices, Uncertainity in Artificial Intelligence.
  6. Deo, N. , 2002, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall of India.
  7. Kumar, A. , Athisayanathan, S. , Antonysamy, A. , 2010, Algorithm to Find All Cliques in a Graph, International Journal of Advanced Networking and Applications, Vol. 02, Issue 02, p. 597-601.
  8. Augustson, J . G. ,. Minker, J. , 1970, An analysis of some graph theoretical cluster techniques, Journal of ACM, Vol. 17, No. 4, p. 571-588.
  9. Mitten, L. G. , Branch and Bound Methods : General Formulation and Properties, 1970, Opns. Res. , Vol. 18, p. 24-34
  10. Coen Bron and Joep Kerboscht, 1937, Finding All Cliques of an Undirected Graph[H], Communications of the ACM, Vol. 16, No. 9, p. 575 - 580.
  11. Baruah, A. K. , Baruah, N. , 2012, Signal Groups of Compatible Graph in Traffic Control Problems, International Journal of Advanced Networking and Applications, Vol. 04, Issue 01, p. 1473-1480.
  12. Chartrand, G. , 1977, Introductory Graph Theory, Dover Publishers, Inc. , New York.
  13. Roberts, F. S. , Graph Theory and Its Application to Social Science, 1978, Regional Conference Series in Applied Mathematics.
Index Terms

Computer Science
Information Sciences

Keywords

Clique Matrix Cycle Time Signal Group Traffic Control Traffic Streams