杜志斌，华南师范大学，副教授、硕士生导师

 

Email: zhibindu@126.com, zhibindu@m.scnu.edu.cn

 

算法分析、渐近分析、分析组合、计数组合学、代数图论、组合矩阵论、化学图论 

 

       发表学术论文130余篇，被SCI收录110余篇，详细发表论文目录可见：

Web of Science Researcher ID: GPT-2615-2022

ResearchGate

MR Author ID: 867883

1. 国家自然科学基金青年科学基金项目，11701505，关于实对称阵的特征值重数的组合性质研究，2018/01–2020/12，25万元，已结题，主持

2. 国家自然科学基金天元基金项目，11426199，实对称阵的伴随图与特征值重数及相关问题的研究，2015/01–2015/12，3万元，已结题，主持

3. 广东省自然科学基金面上项目，2023A1515011472，基于组合多项式系数的渐近分布理论，2023/01–2025/12，10万元，在研，主持

4. 广东省自然科学基金博士启动项目，2014A030310277，基于图的邻接谱与Laplacian谱的图不变量的研究，2015/01–2018/01，10万元，已结题，主持

5. 中国博士后科学基金面上资助，2021M701277，组合统计量的渐近分布理论研究，2021/11 –2022/09，8万元，在研，主持

6. 广东省教育厅青年创新人才项目，2014KQNCX224，图的Estrada指数与Laplacian Estrada指数的极值研究，2015/01–2017/01，7万元，已结题，主持

7. 广东省青年优秀科研人才国际培养计划博士后项目，2022/01–2022/12，10万元，在研，主持

8. 广州市基础研究计划基础与应用基础研究项目，202102080410，实零点方法在概率分布的渐近行为中的应用及其推广，2021/04–2023/03，5万元，在研，主持

9. 佛山市高等教育高层次人才科研项目，2022/10-2025/10，50万，在研，主持

2007-09至2010-06，华南师范大学，数学科学学院，理学硕士，导师：周波 教授

2010-09至2013-06，同济大学，数学系，理学博士  ，导师：邵嘉裕 教授

 

2013-07至2020-06，肇庆学院，数学与统计学院，讲师、副教授

2018-07至2020-06，台湾“中央”研究院，数学研究所，博士后，合作导师：叶永南 研究员

2020-09至现在，华南师范大学，软件学院，特聘研究员、副教授

 

2008

[1] B. Zhou, Z. Du, N. Trinajstić, Harary index of landscape graphs, Int. J. Chem. Model. 1 (2008) 35–44.

2009

[2] Z. Du, B. Zhou, On the reverse Wiener indices of unicyclic graphs, Acta Appl. Math., 106 (2009) 293–306.

[3] Z. Du, B. Zhou, A note on Wiener indices of unicyclic graphs, Ars Combin. 93 (2009) 97–103.

[4] Z. Du, B. Zhou, N. Trinajstić, On Randić indices of chemical trees and chemical unicyclic graphs, MATCH Commun. Math. Comput. Chem. 62 (2009) 131–142.

[5] B. Zhou, I. Gutman, B. Furtula, Z. Du, On two types of geometric-arithmetic index, Chem. Phys. Lett. 482 (2009) 153–155.

2010

[6] Z. Du, B. Zhou, Minimum Wiener indices of trees and unicyclic graphs of given matching number, MATCH Commun. Math. Comput. Chem. 63 (2010) 101–112.

[7] B. Zhou, X. Cai, Z. Du, On Szeged indices of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 113–132. 

[8] B. Zhou, Z. Du, On eccentric connectivity index, MATCH Commun. Math. Comput. Chem. 63 (2010) 181–198.

[9] Z. Du, B. Zhou, N. Trinajstić, Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number, J. Math. Chem. 47 (2010) 842–855.

[10] Z. Du, B. Zhou, N. Trinajstić, Minimum general sum-connectivity index of unicyclic graphs, J. Math. Chem. 48 (2010) 697–703.

[11] R. Xing, B. Zhou, Z. Du, Further results on atom–bond connectivity index of trees, Discrete Appl. Math. 158 (2010) 1536–1545.

[12] Z. Du, B. Zhou, Degree distance of unicyclic graphs, Filomat, 24:4 (2010) 95–120.

[13] B. Zhou, Z. Du, Some lower bounds for Estrada index, Iranian J. Math. Chem. 1 (2010) 67–72.

2011

[14] Z. Du, B. Zhou, On Randić indices of trees, unicyclic graphs and bicyclic graphs, Int. J. Quantum. Chem. 111 (2011) 2760–2770.

[15] Z. Du, B. Zhou, Maximum degree distance of graphs with exactly two      cycles, Bull. Math. Soc. Sci. Math. Roumanie 54 (2011) 119–136.

[16] Z. Du, B. Zhou, N. Trinajstić, On general sum-connectivity index of trees, Appl. Math. Lett. 24 (2011) 402–405.

[17] J. Shao, F. Gong, Z. Du, Extremal energies of weighted trees and forests with fixed total weight sum, MATCH Commun. Math. Comput. Chem. 66 (2011) 879–890.

[18] Z. Du, B. Zhou, N. Trinajstić, On geometric-arithmetic indices of (molecular) trees, unicyclic graphs and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 681–697.

[19] Z. Du, B. Zhou, The Estrada index of trees, Linear Algebra Appl. 435 (2011)    2462–2467.

[20] Z. Du, Z. Liu, On the Estrada and Laplacian Estrada indices of graphs, Linear Algebra Appl. 435 (2011) 2065–2076.

[21] Z. Du, B. Zhou, On the Estrada index of graphs with given number of cut edges, Elec. J. Linear Algebra 22 (2011) 586–592.

2012

[22] W. Luo, B. Zhou, N. Trinajstić, Z. Du, Reverse Wiener indices of graphs of exactly two cycles, Utilitas Math. 88 (2012) 189–202.

[23] Z. Du, B. Zhou, On sum-connectivity index of bicyclic graphs, Bull.  Malaysian Math. Sci. Soc. 35 (2012) 101–117.

[24] Z. Du, On Wiener indices of trees and monocyclic graphs with given bipartition, Int. J. Quantum. Chem., 112 (2012) 1598–1605.

[25] Z. Du, More on Laplacian Estrada indices of trees, Filomat, 26:1 (2012) 197–207.

[26] Z. Du, B. Zhou, The Estrada index of unicyclic graphs, Linear Algebra Appl. 436 (2012) 3149–3159.

[27] Z. Du, B. Zhou, Upper bounds on the sum of Laplacian eigenvalues of graphs, Linear Algebra Appl. 436 (2012) 3672–3683.

[28] Z. Du, B. Zhou, R. Xing, On maximum Estrada indices of graphs with given parameters, Linear Algebra Appl. 436 (2012) 3767–3772.

[29] Z. Du, B. Zhou, N. Trinajstić, Extremal properties of the Zagreb eccentricity indices, Croat. Chem. Acta 85 (2012) 359–362.

2013

[30] Z. Du, A. Ilić, On AGX conjectures regarding average eccentricity, MATCH Commun. Math. Comput. Chem. 69 (2013) 597–609.

[31] Z. Du, An edge grafting theorem on Estrada index of graphs and its applications, Discrete Appl. Math. 161 (2013) 134–139.

[32] Z. Du, C.M. da Fonseca, The singular acyclic matrices with maximal number of P-vertices, Linear Algebra Appl. 438 (2013) 2274–2279.

[33] Z. Du, A. Ilić, L. Feng, Further results on the distance spectral radius of graphs, Linear Multilinear Algebra 61 (2013) 1287–1301.

[34] Z. Du, B. Zhou, Reverse degree distances of unicyclic graphs, Bull. Iranian Math. Soc. 39 (2013) 681–706.

2014

[35] Z. Du, C.M. da Fonseca, Nonsingular acyclic matrices with an extremal number of P-vertices, Linear Algebra Appl. 442 (2014) 2–19.

2015

[36] Z. Du, C.M. da Fonseca, The acyclic matrices with a P-set of maximum size, Linear Algebra Appl. 468 (2015) 27–37.

[37] L. Zhou, B. Zhou, Z. Du, On the number of Laplacian eigenvalues of trees smaller than two, Taiwanese J. Math. 19 (2015) 65–75.

[38] Z. Du, On the atom-bond connectivity index and radius of connected graphs, J. Ineq. Appl. 2015 (2015) 188.

[39] Z. Du, C.M. da Fonseca, The singular acyclic matrices with the second largest number of P-vertices, Linear Multilinear Algebra 63 (2015) 2103–2120. 

2016

[40] Z. Du, A. Ilić, A proof of the conjecture regarding the sum of domination number and average eccentricity, Discrete Appl. Math. 201 (2016) 105–113. 

[41] Z. Du, C.M. da Fonseca, On a family of trees with minimal atom-bond connectivity index, Discrete Appl. Math. 202 (2016) 37–49. 

[42] D. Dimitrov, Z. Du, C.M. da Fonseca, On structural properties of trees with minimal atom-bond connectivity index III: Trees with pendent paths of length three, Appl. Math. Comput. 282 (2016) 276–290. 

[43] X. Qi, B. Zhou, Z. Du, The Kirchhoff indices and the matching numbers of unicyclic graphs, Appl. Math. Comput. 289 (2016) 464–480. 

[44] Z. Du, C.M. da Fonseca, The real symmetric matrices of odd order with a P-set of maximum size, Czechoslovak Math. J. 66 (2016) 1007–1026.

[45] Z. Du, C.M. da Fonseca, The Bruhat rank of a binary symmetric staircase pattern, Open Math. 14 (2016) 832–840.

[46] Z. Du, C.M. da Fonseca, The singular acyclic matrices of even order with a P-set of maximum size, Filomat 30 (2016) 3403–3409. 

[47] Z. Du, The least eigenvalues of unicyclic graphs, Ars Combin. 125 (2016) 109–119. 

2017

[48] Z. Du, Asymptotic Expressions for resolvent energies of paths and cycles, MATCH Commun. Math. Comput. Chem. 77 (2017) 85–94. 

[49] Z. Du, Further results regarding the sum of domination number and average eccentricity, Appl. Math. Comput. 294 (2017) 299–309. 

[50] X. Qi, Z. Du, On Zagreb eccentricity indices of trees, MATCH Commun. Math. Comput. Chem. 78 (2017) 241–256. 

[51] Z. Du, Spectral properties of a class of unicyclic graphs, J. Ineq. Appl. 2017 (2017) 96. 

[52] N.H.M. Husin, R. Hasni, Z. Du, On extremum geometric-arithmetic indices of (molecular) trees, MATCH Commun. Math. Comput. Chem. 78 (2017) 375–386. 

[53] A. Ali, Z. Du, On the difference between atom-bond connectivity index and Randić index of binary and chemical trees, Int. J. Quantum. Chem. 117 (2017) e25446. 

2018

[54] Z. Du, A. Ali, The inverse Wiener polarity index problem for chemical trees, PLoS ONE 13 (2018) e0197142. 

[55] H. Lin, Z. Du, B. Zhou, On the first two largest distance Laplacian eigenvalues of unicyclic graphs, Linear Algebra Appl. 546 (2018) 289–307. 

[56] D. Dimitrov, Z. Du, C.M. da Fonseca, The minimal-ABC trees with  -branches, PLoS ONE 13 (2018) e0195153. 

[57] A. Ali, Z. Du, M. Ali, A note on chemical trees with minimum Wiener polarity index, Appl. Math. Comput. 335 (2018) 231–236. 

[58] D. Dimitrov, Z. Du, C.M. da Fonseca, Some forbidden combinations of branches in minimal-ABC trees, Discrete Appl. Math. 236 (2018) 165–182.

[59] N.H.M. Husin, R. Hasni, Z. Du, A. Ali, More results on extremum Randić indices of (molecular) trees, Filomat 32 (2018) 1075–1083. 

[60] Z. Du, D. Dimitrov, The minimal-ABC trees with  -branches II, IEEE Access 6 (2018) 66350–66366. 

[61] Z. Du, A diagonalization algorithm for the distance matrix of cographs, IEEE Access 6 (2018) 74931–74939. 

2019

[62] Z. Du, A. Ali, The alkanes with maximum Wiener polarity index, Mol. Inform. 38 (2019) 1800076. 

[63] Z. Du, A. Ali, N. Trinajstić, Alkanes with the first three maximal/minimal modified first Zagreb connection indices, Mol. Inform. 38 (2019) 1800116. 

[64] A. Ali, D. Dimitrov, Z. Du, F. Ishfaq, On the extremal graphs for general sum-connectivity index ( ) with given cyclomatic number when  , Discrete Appl. Math. 257 (2019) 19–30. 

[65] Z. Du, C.M. da Fonseca, The number of P-vertices for acyclic matrices of maximum nullity, Discrete Appl. Math. 269 (2019) 211–219. 

[66] Z. Du, C.M. da Fonseca, On the continuity of the maximum size of P-sets of acyclic matrices, Discrete Math. 342 (2019) 2278–2282. 

[67] Z. Du, The sum of the first two largest signless Laplacian eigenvalues of trees and unicyclic graphs, Elec. J. Linear Algebra 35 (2019) 449–467. 

[68] A. Ali, S. Ahmed, Z. Du, W. Gao, M.A. Malik, On the minimal general sum-connectivity index of connected graphs without pendant vertices, IEEE Access 7 (2019) 136743–136751. 

[69] A. Ali, Z. Du, K. Shehzadi, Estimating Some general molecular descriptors of saturated hydrocarbons, Mol. Inform. 38 (2019) 1900007. 

2020

[70] Z. Du, D. Dimitrov, The minimal-ABC trees with  -branches, Comput. Appl. Math. 39 (2020) 85. 

[71] Z. Du, C.M. da Fonseca, L. Losonczi, On nonsingular acyclic M-matrices whose inverse is also acyclic, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 114 (2020) 138. 

[72] Z. Du, C.M. da Fonseca, The number of P-vertices of singular acyclic matrices: An inverse problem, Discuss. Math. Graph Theory 40 (2020) 525–532. 

[73] Z. Du, J. Yeh, Another simple proof of Graham and Pollak's theorem, Discrete Math. 343 (2020) 111994. 

[74] M. Andelić, Z. Du, C.M. da Fonseca, E. Kilić, A matrix approach to some second-order difference equations with sign-alternating coefficients, J. Difference Equ. Appl. 26 (2020) 149–162. 

[75] M. Andelić, Z. Du, C.M. da Fonseca, S.K. Simić, Tridiagonal matrices and spectral properties of some graph classes, Czechoslovak Math. J. 70 (2020) 1125–1138

[76] X. Qi, Z. Du, X. Zhang, Extremal properties of Kirchhoff index and degree resistance distance of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 84 (2020) 671–690. 

[77] N.H.M. Husin, Z. Du, R. Hasni, Unicyclic graphs with maximum geometric-arithmetic indices, Ars Combin. 148 (2020) 89–107. 

[78] Y. Amanbek, Z. Du, Y. Erlangga, C.M. da Fonseca, B. Kurmanbek, A. Pereira, Explicit determinantal formula for a class of banded matrices, Open Math. 18 (2020) 1227–1229. 

[79] Z. Du, C.M. da Fonseca, On the Bruhat rank of a Boolean F-matrix, Bull. Math. Soc. Sci. Math. Roumanie 63 (2020) 43–49.

[80] A. Jahanbani, R. Hasni, Z. Du, S.M. Sheikholeslami, Spectral properties with the difference between topological indices in graphs, J. Math. 2020 (2020) 6973078. 

[81] W.N.N.N.W. Zuki, Z. Du, M.K. Jamil, R. Hasni, Extremal trees with respect to the difference between atom-bond connectivity index and Randić index, Symmetry 12 (2020) 1591.

2021

[82] Z. Du, Coulson-type integral formulas for the sum of powers of absolute values of roots of polynomials, J. Math. Anal. Appl. 494 (2021) 124650. 

[83] Y. Yuan, Z. Du, The first two maximum ABC spectral radii of bicyclic graphs, Linear Algebra Appl. 615 (2021) 28–41. 

[84] D. Dimitrov, Z. Du, A solution of the conjecture about big vertices of minimal-ABC trees, Appl. Math. Comput. 397 (2021) 125818. 

[85] Z. Du, B. Zhou, On quotient of geometric–arithmetic index and square of spectral radius, MATCH Commun. Math. Comput. Chem. 85 (2021) 77–86.

[86] A. Jahanbani, M. Atapour, Z. Du, New results on the geometric-arithmetic index, J. Math. 2021 (2021) 4901484.

[87] Y. Yuan, B. Zhou, Z. Du, On large ABC spectral radii of unicyclic graphs, Discrete Appl. Math. 298 (2021) 56-65.

[88] Z. Du, K.C. Das, The conjecture about the comparison for resolvent energies of cycles and stars, MATCH Commun. Math. Comput. Chem. 86 (2021) 635–641.

[89] A. Ali, Z. Du, S.S. Zaineb, T. Alraqad, On the second maximum Wiener polarity index of chemical trees of a fixed order, Int. J. Quantum. Chem. 121 (2021) e26631.

[90] Z. Du, A. Ali, R. Rafee, Z. Raza, M.K. Jamil, On the first two extremum Zagreb indices and coindices of chemical trees, Int. J. Quantum. Chem. 121 (2021) e26547.

[91] Z. Du, C.M. da Fonseca, Y. Xu, J. Ye, Disproving a conjecture of Thornton on Bohemian matrices, Open Math. 19 (2021) 505–514. 

2022

[92] Z. Du, D. Dimitrov, C.M. da Fonseca, New strong divisibility sequences, Ars Math. Contemp. 22 (2022) #P1.08.

[93] Z. Du, C.M. da Fonseca, A. Pereira, On determinantal recurrence relations of banded matrices, Kuwait J. Sci. 49 (2022) 1–9.

[94] Z. Du, A.A.S.A. Jamri, R. Hasni, D.A. Mojdeh, Maximal first Zagreb index of trees with given Roman domination number, AIMS Math. 7 (2022) 11801–11812.

[95] Z. Du, Y. Xu, A generalization of Alon–Aydinian–Huang theorem, Discrete Math. 345 (2022) 112968. 

[96] Z. Du, Y. Huang, The multiplicity of eigenvalues of trees, Linear Algebra Appl. 654 (2022) 56–68.

[97] Z. Du, C.M. da Fonseca, A periodic determinantal property for (0,1) double banded matrices, Linear Multilinear Algebra 70 (2022) 5316–5328.

[98] Z. Du, C.M. da Fonseca, An identity involving derangement numbers and Bell numbers, Appl. Anal. Discrete Math. 16 (2022) 485–494.

2023

[99] Z. Du, The asymptotic normality of adjacency coefficients of bipartite graphs and skew-adjacency coefficients of oriented graphs, Linear Algebra Appl. 656 (2023) 541–558.

[100] A.M. Albalahi, A. Ali, Z. Du, A.A. Bhatti, T. Alraqad, N. Iqbal, A.E. Hamza, On bond incident degree indices of chemical graphs, Math. 11 (2023) 27.

[101] Z. Du, C.M. da Fonseca, Root location for the characteristic polynomial of a Fibonacci type sequence, Czechoslovak Math. J. 73 (2023) 189–195.

[102] Z. Du, T.-W. Chao, Y.-N. Yeh, Several improved asymptotic normality criteria and their applications to graph polynomials, Discrete Math. 346 (2023) 113303.

[103] Z. Du, R. Xing, The Graham-Hoffman-Hosoya type theorems for the exponential distance matrix, Elec. J. Linear Algebra 39 (2023) 62–70.

[104] R. Xing, Z. Du, The exponential distance matrix of block graphs, Appl. Math. Comput. 447 (2023) 127673.

[105] Z. Du, B. Zhou, On the ABC spectral radius of cactus graphs, Oper. Matrices 17 (2023) 57–68.

[106] Z. Du, Y. Huang, The multiplicity of eigenvalues of unicyclic graphs, Linear Algebra Appl. 670 (2023) 19–41.

[107] D. Dimitrov, Z. Du, Complete characterization of the minimal-ABC trees, Discrete Appl. Math. 336 (2023) 148–194.

[108] Z. Du, C.M. da Fonseca, V. Kowalenko, Further developments of basic trigonometric power sums, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 117 (2023) 112. 

[109] Z. Du, C.M. da Fonseca, The characterization of the minimal weighted acyclic graphs, Linear Algebra Appl. 672 (2023) 75–92.

[110] R. Xing, Z. Du, A q-analogue of distance matrix of block graphs, Advances Appl. Math. 149 (2023) 102548. 

[111] J. Chen, B. Zeng, Z. Du, H. Deng, M. Xu, Z. Gan, M. Ding, RFM: response-aware feedback mechanism for background based conversation, Appl. Intell. 53 (2023) 10858–10878.

[112] Z. Du, C.M. da Fonseca, The number of P-vertices for acyclic matrices with given nullity, Discrete Math. 346 (2023) 113592. 

[113] Z. Du, C.M. da Fonseca, The determinants of certain double banded (0,1) Toeplitz matrices, Miskolc Math. Notes 24 (2023) 1307–1315. 

[114] A.M. Albalahi, Z. Du, A. Ali, On the general atom-bond sum-connectivity index, AIMS Math. 8 (2023) 23771–23785. 

2024

[115] D. Dimitrov, Z. Du, The ABC index conundrum's complete solution, MATCH Commun. Math. Comput. Chem. 91 (2024) 5–38.

[116] Z. Du, C.M. da Fonseca, “The periodic determinantal property for (0, 1) double banded matrices”: A correction and some comments, Linear Multilinear Algebra 72 (2024) 1254–1258.

[117] Z. Du, Y. Huang, Some extensions of Collatz (periodic) conjecture, Appl. Math. Comput. 475 (2024) 128742.

[118] A.M. Albalahi, Z. Du, A. Ali, A.M. Alanazi, On the graphs of a fixed cyclomatic number and order with minimum general sum-connectivity and Platt indices, Comput. Appl. Math. 43 (2024) 137.

[119] L. He, B. Chen, Q. Liu, H. Chen, H. Li, W. Chow, J. Tang, Z. Du, Y. He, J. Pan, A quasi-exponential distribution of interfacial voids and its effect on the interlayer strength of 3D printed concrete, Addit. Manuf. 89 (2024) 104296.

[120] J. Cooper, Z. Du, Note on the spectra of Steiner distance hypermatrices, Electron. J. Combin. 31 (2024) 34.

[121] Z. Du, C.M. da Fonseca, Sylvester-Kac matrices with quadratic spectra: A comprehensive note, Ramanujan J. 65 (2024) 1313–1322.

2025

[122] Z.-B. Du, Z.-M. Zhou, H.-Y. Shan, C.-X. He, Corrigendum to “On the sum of the first two largest signless Laplacian eigenvalues of a graph” [Discrete Math. 347 (2024) 114035], Discrete Math. 348 (2025) 114241.

[123] Z. Du, When (signless) Laplacian coefficients meet matchings of subdivision, European J. Combin. 124 (2025) 104087.

[124] Z. Du, C.M. da Fonseca, A note on the eigenvalues of a Sylvester-Kac type matrix with off-diagonal biperiodic perturbations, J. Comput. Appl. Math. 461 (2025) 116429.