|
给定图的距离熵及其应用
|
Abstract:
图熵是图的信息理论测度,近年来,图熵慢慢成为测量图的结构信息测度的载体,距离是最重要的图不变量之一。本文主要研究了树和化学树的距离熵及其相关应用,并且研究了给定图在笛卡尔积、强积和冠积运算下的距离熵值。
Graph entropy is the information theory measure of graphs. In recent years, graph entropy has gradually become the carrier to measure the structure information of graphs, and distance is one of the most important graph invariants. In this paper, we mainly study the range entropy of tree and chemical tree and its related applications, and study the range entropy of given graph under Cartesian product, strong product and crown product operations.
[1] | Chen, Z., Dehmer, M. and Shi, Y. (2014) A Note on Distance-Based Graph Entropies. Entropy, 16, 5416-5427. https://doi.org/10.3390/e16105416 |
[2] | Shannon, C.E. (1948) A Mathematical Theory of Communication. Bell System Technical Journal, 27, 379-423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x |
[3] | Dehmer, M. and Mowshowitz, A. (2011) A History of Graph Entropy Measures. Information Sciences, 181, 57-78. https://doi.org/10.1016/j.ins.2010.08.041 |
[4] | Ghorbani, M., Dehmer, M. and Zangi, S. (2018) Graph Operations Based on Using Distance-Based Graph Entropies. Applied Mathematics and Computation, 333, 547-555. https://doi.org/10.1016/j.amc.2018.04.003 |
[5] | Dong, Y. and Cambie, S. (2022) On the Main Distance-Based Entropies: The Eccentricity-and Wiener-Entropy. arXiv Preprint arXiv:2208.12209 |
[6] | Noureen, S., Bhatti, A.A. and Ali, A. (2021) A Note on the Minimum Wiener Polarity Index of Trees with a Given Number of Vertices and Segments or Branching Vertices. Discrete Dynamics in Nature and Society, 2021, Article ID: 1052927. https://doi.org/10.1155/2021/1052927 |
[7] | Ali, A., Du, Z. and Ali, M. (2018) A Note on Chemical Trees with Minimum Wiener Polarity Index. Applied Mathematics and Computation, 335, 231-236. https://doi.org/10.1016/j.amc.2018.04.051 |
[8] | Dehmer, M., Emmert-Streib, F. and Shi, Y. (2014) Interrelations of Graph Distance Measures Based on Topological Indices. PLOS ONE, 9, e94985. https://doi.org/10.1371/journal.pone.0094985 |
[9] | Deng, H. (2011) On the Extremal Wiener Polarity Index of Chemical Trees. MATCH Communications in Mathematical and in Computer Chemistry, 66, 305-314. |
[10] | Yue, J., Lei, H. and Shi, Y. (2018) On the Generalized Wiener Polarity Index of Trees with a Given Diameter. Discrete Applied Mathematics, 243, 279-285. https://doi.org/10.1016/j.dam.2018.02.003 |
[11] | Liu, B., Hou, H. and Huang, Y. (2010) On the Wiener Polarity Index of Trees with Maximum Degree or Given Number of Leaves. Computers & Mathematics with Applications, 60, 2053-2057. https://doi.org/10.1016/j.camwa.2010.07.045 |
[12] | Deng, H. and Xiao, H. (2010) The Maximum Wiener Polarity Index of Trees with k Pendants. Applied Mathematics Letters, 23, 710-715. https://doi.org/10.1016/j.aml.2010.02.013 |
[13] | Khalifeh, M.H., Yousefi-Azari, H. and Ashrafi, A.R. (2008) The Hyper-Wiener Index of Graph Operations. Computers & Mathematics with Applications, 56, 1402-1407. https://doi.org/10.1016/j.camwa.2008.03.003 |
[14] | Yero, I.G. and Rodríguez-Velázquez, J.A. (2011) On the Randi? Index of Corona Product Graphs. ISRN Discrete Mathematics, 2011, Article ID: 262183. https://doi.org/10.5402/2011/262183 |
[15] | Dehmer, M., Varmuza, K., Borgert, S. and Emmert-Streib, F. (2009) On Entropy-Based Molecular Descriptors: Statistical Analysis of Real and Synthetic Chemical Structures. Journal of Chemical Information and Modeling, 49, 1655-1663. https://doi.org/10.1021/ci900060x |
[16] | Imrich, W., Klav?ar, S. and Hammack, R.H. (2000) Product Graphs: Structure and Recognition. John Wiley & Sons Ltd. |
[17] | Dobrynin, A.A., Entringer, R. and Gutman, I. (2001) Wiener Index of Trees: Theory and Applications. Acta Applicandae Mathematicae, 66, 211-249. https://doi.org/10.1023/a:1010767517079 |
[18] | Hrinakova, K., et al. (2014) A Congruence Relation for the Wiener Index of Graphs with a Tree-Like Structure. MATCH Communications in Mathematical and in Computer Chemistry, 72, 791-806. |
[19] | Ma, J., Shi, Y. and Yue, J. (2014) On the Extremal Wiener Polarity Index of Unicyclic Graphs with a Given Diameter. In: Gutman, I., Ed., Topics in Chemical Graph Theory, Mathematical Chemistry Monographs, University of Kragujevac and Faculty of Science Kragujevac, 177-192. |
[20] | Liu, M. and Liu, B. (2011) On the Wiener Polarity Index. MATCH Communications in Mathematical and in Computer Chemistry, 66, 293-304. |
[21] | Ma, J., Shi, Y., Wang, Z. and Yue, J. (2016) On Wiener Polarity Index of Bicyclic Networks. Scientific Reports, 6, Article No. 19066. https://doi.org/10.1038/srep19066 |