Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 4 (2009), 169 -- 177

ENTROPY DUE TO FRAGMENTATION OF DENDRIMERS

Lorentz Jäntschi and Sorana D. Bolboacă

Abstract. Subgraphs can results through application of criteria based on matrix which characterize the entire graph. The most important categories of criteria are the ones able to produce connected subgraphs (fragments). Based on theoretical frame on graph theory, the fragmentation algorithm on pair of vertices containing the largest fragments (called MaxF) are exemplified. The counting polynomials are used to enumerate number of all connected substructures and their sizes. For a general class of graphs called dendrimers general formulas giving counting polynomials are obtained and characterized using informational measures.

2000 Mathematics Subject Classification: 05C10; 11T06.
Keywords: Graph theory; Subgraphs; Graph polynomials; Entropy.

Full text



Acknowledgement. This work was supported by UEFISCSU Romania through grants (ID0458/206/2007 and ID1051/202/2007).

References

  1. S. D. Bolboacă and L. Jäntschi, How Good the Characteristic Polynomial Can Be for Correlations?, International Journal of Molecular Sciences, 8 (2007), 335-345. DOI 10.3390/i8040335.

  2. L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, Wiener Berichte, 66 (1872), 275-370. JFM 04.0566.01.

  3. M. V. Diudea, I. Gutman and L. Jäntschi, Molecular Topology, Nova Science Publishers, 2001, LoC 2001031282.

  4. M. V. Diudea and C. L. Nagy, Counting polynomials on nanostructures. In: Periodic Nanostructures. Series: Developments in Fullerene Science, 7 (2007), 69-114. DOI 10.1007/978-1-4020-6020-5_4.

  5. M. V. Diudea, A. E. Vizitiu and D. Janezic, Cluj and related polynomials applied in correlating studies, Journal of Chemical Information and Modeling, 47 (2007), 864-874. DOI 10.1021/ci600482j.

  6. L. Jäntschi, S. D. Bolboacă and C. M. Furdui, Characteristic and Counting Polynomials: Modelling Nonane Isomers Properties, Molecular Simulation, 35 (2009), 220-227. DOI 10.1080/08927020802398892.

  7. L. Jäntschi and M. V. Diudea, Subgraphs of pair vertices, Journal of Mathematical Chemistry, 45 (2009), 364-371. MR2470467. Zbl 1171.05433.

  8. J. F. Ragot, Counting Polynomials with Zeros of Given Multiplicities in Finite Fields, Finite Fields and Their Applications, 5 (1999), 219-231. MR1702893. Zbl 1024.11076.

  9. A. Rényi, On measures of information and entropy, Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 1 (1961), 547-561. MR0132570(24 #A2410). Zbl 0106.33001.

  10. C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, 27(1948), 379-423 and 623-656. MR0026286(10,133e). Zbl 1154.94303.

  11. E. H. Simpson, Measurement of Diversity, Nature 163 (1949), 688-688. Zbl 0032.03902.

  12. R. P. Stanley, Enumerative Combinatorics (I and II), In: Cambridge Studies in Advanced Mathematics, 49 and 62, 1997 and 1999. MR1442260(98a:05001) and MR1676282(2000k:05026). Zbl 0945.05006 and Zbl 0978.05002.






Lorentz Jäntschi
Faculty of Materials Science and Engineering, Technical University of Cluj-Napoca,
400641 Cluj, Romania.
e-mail: lori@academicdirect.org
http://lori.academicdirect.org

Sorana D. Bolboacă
Department of Medical Informatics and Biostatistics,
"Iuliu Haţieganu" University of Medicine and Pharmacy,
400349 Cluj, Romania.
e-mail: sorana@j.academicdirect.org
http://sorana.academicdirect.ro

http://www.utgjiu.ro/math/sma