Research Article | OPEN ACCESS
Construction of Measurable Incidence and Adjacency Matrices from Product Measures
1, 2Amadu Fullah Kamara and 2Mohamed Abdulai Koroma
1Department of Mathematics, University of Science and Technology of China, Hefei, China
2Department of Mathematics, Faculty of Pure and Applied Sciences, Fourah Bay College, University of Sierra Leone, Freetown, Sierra Leone
Research Journal of Applied Sciences, Engineering and Technology 2014 6:1236-1239
Received: March 29, 2013 | Accepted: April 22, 2013 | Published: February 15, 2014
Abstract
This study presents a new method of representing graphs and a new approach of constructing both incidence and adjacency matrices using the theory of product measures. It further shows that matrices constructed by this approach are measurable which a major advantage of this method is.
Keywords:
Adjacency matrix, incidence matrix, product measures, measures,
References
-
Agaian, S.S., 1985. Hadamard Matrices and their Applications. Springer-Verlag, Berlin, pp: 227.
CrossRef
-
Ando, T., 1989. Majorization, doubly stochas-tic matrices and comparison of eigenval-ues. Linear Algebra Appl., 118: 163-248.
CrossRef -
Balakrishnan, R. and K. Ranganathan, 2000. A Textbook of Graph Theory. Springer-Verlag, Berlin, Heidelberg, pp. 1-12.
CrossRef -
Berberian, S.K., 1999. Fundamentals of Real Analysis. Springer-Verlag, New York Inc., pp: 86-97.
-
Bhatia, R., 1997. Matrix Analysis. Springer-Verlag, New York.
CrossRef -
Bhatia, R., 2007. Positive Definite Matrices. Princeton University Press, Princeton, N.J.
-
Borwein, J.M. and A.S. Lewis, 2000. Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer, New York, pp: 310.
CrossRef -
Brauer, A. and I.C. Gentry, 1968. On the characteristic roots of tournament matrices. Bull. Amer. Math. Soc., 74: 1133-1135.
CrossRef -
Chen, C. and F.K. Hwang, 2000. Minimum distance diagram of double- loop net- works. IEEE T. Comput., 49: 977-979.
CrossRef -
Diestel, R., 2006. Graph Theory. 3rd Edn., Springer-Verlag, Berlin, Heidelberg, pp: 28.
-
Fiedler, M., 1971. Bounds for the determinant of the sum of two Hermitian matrices. Proc. Amer. Math. Soc., 30: 27-31.
CrossRef -
Friedman, A., 1982. Foundations of Modern Analysis. Dover Publications Inc., New York, pp: 78-83.
PMid:10256765 -
Hewitt, E. and K. Stromberg, 1965. Real and Abstract Analysis. Graduate Texts in Mathematics. Springer-Verlag, Berlin, Heidelberg, pp: 125-141.
CrossRef -
Lieb, E.H. and M. Loss, 2001. Analysis. 2nd Edn., American Mathematical Society, Providence, Rhode Island, pp: 4-12.
CrossRef -
Li, F., W. Wang, Z. Xu and H. Zhao, 2011. Some results on the lexicographic product of vertex-transitive graphs. Appl. Math. Lett., 24: 1924-1926.
CrossRef -
Mandl, C., 1979. Applied Network Optimization. Academic Press Inc., Ltd., London.
-
Schrijver, A., 2009. A Course in Combinatorial Optimization.
Direct Link -
Strayer, J.K., 1992. Linear Programming and Its Applications. World Publishing Corporation, Beijing, pp: 140-231.
-
Xu, J., 2001. Combinatorial Theory in Networks. Kluwer Academic Publishers, pp: 73-83.
-
Xu, J., 2003. Theory and Application of Graphs. Springer, Dordrecht, pp: 334.
CrossRef
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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