劉木伙 (Muhuo Liu) 簡歷
華南農業大學，數學與信息(軟件)學院，副教授，碩士研究生導師
男，1981年3月生，2014年于南京師范大學獲理學博士學位，美國Mathematical Reviews評論員，主要從事結構圖論和圖譜理論等方面的研究，在《中國科學》、《J. Combin. Theory Ser. A》、《Adv. in Appl. Math.》《European J. Combin.》、《Electron. J. Combin.》、《J. Algebraic Combin.》、《Discrete Math.》、《Discrete Appl. Math.》、《Linear Algebra Appl.》、《Linear Multilinear Algebra》、《Graphs Combin.》等國內外數學學術刊物上發表或被接受科研論文100多篇，其中100多篇發表或被接受在SCI刊源期刊上。第一作者編寫的專著《圖譜的極值理論》于2017年由廣東省科技出版社出版，其英文版于2018年由University of Kragujevac and Faculty of Science Kragujevac出版社出版。
曾經參加或主持國家自然科學基金、國家自然科學青年基金、江蘇省自然科學基金等項目的研究。于2010年入選華南農業大學青年骨干教師培養對象，2011年入選南京師范大學博士學術新人培養計劃，2013年獲博士研究生國家獎學金，2014年入選廣東省高等學校“千百十人才培養工程”第八批校級培養對象，2015年入選廣東省高等學校優秀青年教師培養計劃。
主持的課題：
(1)廣東高校優秀青年創新人才培養計劃項目(No. LYM10039,主持): 圖論的理論及其應用的研究，2011.01--2012.12；
(2)國家自然科學青年基金(11201156，主持)：圖譜理論中若干問題的研究，2013.01-2015.12;
(3)2015年度廣東省優秀青年教師培養計劃(YQ2015027,主持)：對最小度有所約束的一些圖的劃分問題，2016.01—2018.12；
(4)廣東省普通高校特色創新項目 （2017KTSCX020，主持）：圖譜的優超理論，2018.01-2019.12. (5)廣東省自然科學基金面上項目 （2022A1515011786，主持）：圖譜確定性的研究，2022.01-2024.12.
(6) 國家自然科學基金面上基金 (12271182，主持 )：關于圖結構的譜刻畫問題的研究，2023.01-2026.12.
(7) 廣東省自然科學基金面上項目 （2024A1515011899，主持）：基于最大和次大鄰接特征值的一些圖譜問題的研究，2024.01-2026.12.
參與的課題：
(1) 廣東省博士啟動基金(No.5300084,排名第五)：組合矩陣論研究，2006.01—2007.12；
(2) 國家自然科學基金數學天元基金項目（No.10526019,排名第五)：組合數學－組合矩陣論研究，2006.01—2006.12；
(3)國家自然科學基金(No. 11071088，排名第三),組合矩陣論的指數理論和譜理論，2011.01-2013.12；
(4)江蘇省自然科學基金(No. BK20131357，排名第三): 圖的拓撲指標與圖參數的極值問題及相關問題,2013.07-2016.06
(5)國家自然科學基金面上基金項目(No. 11571123，排名第三):張量的本原性、本原指數及張量與超圖譜若干問題的研究，2016/01-2019/12
專著與教材：
(1) 劉木伙,柳柏濂，《圖譜的極值理論》, 廣東科技出版社，2017年.
(2) M.Liu, B.Liu, 《Extremal Theory of Graph Spectrum》，University of Kragujevac and Faculty of Science, 2018.
(3) 劉木伙主編，《線性代數》，湖南大學出版社, 2023.
(I) 代表論文：
[1] M. Liu, X. Gu, Spectral characterization of the complete graph removing a path: Completing the proof of C\'amara-Haemers Conjecture, Discrete Math., 344 (2021), 112-275. (SCI)
[2] M. Liu, B. Xu, On a conjecture of Schweser and Stiebitz, Discrete Appl. Math., 295 (2021) 25–31. (SCI)
[3] M. Liu, C. Chen, Z. Stani?, On graphs whose second largest eigenvalue is at most 1, European J. Combin., 97 (2021) 103385. (SCI)
[4] B. Cheng, M. Liu (Corresponding author), B.-S. Tam, On the nullity of a connected graph in terms of order and maximum degree, Linear Algebra Appl., 632 (2022) 193–232. (SCI)
[5] X. Gu, M. Liu, A tight lower bound on the matching number of graphs via Laplacian eigenvalues, European J. Combin., 101 (2022) 103468. (SCI)
[6] M. Liu, C. Chen, Z. Stani?, Connected (K_4-e)-free graphs whose second largest eigenvalue does not exceed 1, European J. Combin., 115 (2024) 103775. (SCI)
[7] M. Liu, X. Gu, H. Shan, Z. Stanic, Spectral characterization of the complete graph removing a cycle, J. Combin. Theory Ser. A, 205 (2024), 105868. (SCI)
[8] M. Zhai, M. Liu (Corresponding author), Extremal problems on planar graphs without k edge-disjoint cycles, Adv. in Appl. Math., 157 (2024) 102701. (SCI)
[9] X. Gu, M. Liu (Corresponding author), A unified combinatorial view beyond some spectral properties, J. Algebraic Combin., 60 (2024), 817–841. (SCI)
[10] M. Liu, C. Chen, Z. Stanic, H. Shan, Graphs with large clique number whose second largest eigenvalue does not exceed $(\sqrt{5}-1)/2$, Electron. J. Combin., 32(2025), #P2.13. (SCI)
(II) 其他的論文：
[1] B. Liu, Liu M., On the spread of the spectrum of a graph, Discrete Math., 309 (2009), 2727-2732. (SCI)
[2] M. Liu, B. Liu, Z. You, The majorization theorem of connected graphs, Linear Algebra Appl., 431 (2009), 553-557. (SCI)
[3] M. Liu, B. Liu, The signless Laplacian spread, Linear Algebra Appl., 432 (2010), 505-514. (SCI)
[4] M. Liu, B. Liu, On the k-th smallest and k-th greatest modified Wiener indices of trees, Discrete Appl. Math., 158 (2010), 699-705. (SCI)
[5] M. Liu, B. Liu, On the spectral radii and the signless Laplacian spectral radii of c-cyclic graphs with fixed maximum degree, Linear Algebra Appl., 435 (2011) 3045-3055. (SCI)
[6] M. Liu, The (signless Laplacian) spectral radii of connected graphs with prescribed degree sequences, Electron. J. Combin., 19(4) (2012), #P35 (SCI)
[7] M. Liu, Lihua You, Bolian Liu, The proof of a conjecture on the lewin number of primitive non-powerful signed digraphs, Linear Algebra Appl., 438 (2013), 2366-2377. (SCI)
[8] K. Ch. Das, K. Xu, M. Liu, On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl., 439 (2013), 3561-3575. (SCI)
[9] M. Liu, B. Liu, The second Zagreb indices of unicyclic graphs with given degree sequences, Discrete Appl. Math., 167 (2014), 217-221. (SCI)
[10] M. Liu, H. Shan, K. Ch. Das, Some graphs determined by their (signless) Laplacian spectra, Linear Algebra Appl., 449 (2014), 154-165. (SCI)
[11] M. Liu, B. Liu, The majorization theorem of extremal pseudographs, Linear Algebra Appl., 459 (2014), 13-22. (SCI)
[12] K. Ch. Das, M. Liu, H. Shan, Upper bounds on the (signless) Laplacian eigenvalues of graphs, Linear Algebra Appl., 459 (2014), 334-341. (SCI)
[13] M. Liu, B. Liu, B. Cheng, Ordering (signless) Laplacian spectral radii with maximum degrees of graphs, Discrete Math., 338 (2015), 159-163. (SCI)
[14] M. Liu, B. Xu, Bipartition of graph under degree constraints, Sci. China Math., 58 (2015), 869–874. (SCI,《中國科學》英文版)
[15] K. Ch. Das, M. Liu, Complete split graph determined by its (signless) Laplacian spectrum, Discrete Appl. Math., 205 (2016), 45-51. (SCI)
[16] H. Shan, M. Liu (Corresponding author), Laplacian spectral radius of c-cyclic graph and maximum vertex degree, Sci Sin Math, (46) 2016, 1227–1240 (中國科學(中文版)
[17] M. Liu, Y. Zhu, H. Shan, K. Ch. Das, The spectral characterization of butterfly-like graphs, Linear Algebra Appl., 513 (2017), 55-68. (SCI)
[18] M. Liu, K. Ch. Das, H. Lai, The spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices, Linear Multilinear Algebra, 65 (2017), 869-881. (SCI)
[19] G. Zhang, M. Liu, H. Shan, Which Q-cospectral graphs have same degree sequences, Linear Algebra Appl., 520 (2017), 274-285. (SCI)
[20] M. Liu, B. Xu, On partitions of graphs under degree constrains, Discrete Appl. Math., 226 (2017) 87-93. (SCI)
[21] M. Liu, Y. Yuan, L. You, Z. Chen, Which cospectral graphs have same degree sequences, Discrete Math., 341 (2018), 2969-2976. (SCI)
[22] M. Liu, K. Xu, X.-D. Zhang, Extremal graphs for vertex-degree-based invariants with given degree sequences, Discrete Appl. Math., 255 (2019) 267-277. (SCI)
[23] Liu, H.-J. Lai, Kinkar Ch. Das, Spectral results on Hamiltonian problem, Discrete Math., 342 (2019) 1718-1730. (SCI)
[24] Y. Yao, M. Liu (Corresponding author), Francesco Belardo, Chao Yang, Unified extremal results of topological indices and spectral invariants of graphs, Discrete Appl. Math., 271 (2019) 218–232. (SCI)
[25] J. Ye, M. Liu (Corresponding author), Y. Yao, K. Ch. Das, Extremal polygonal cacti for bond Incident degree indices, Discrete Appl. Math., 257 (2019), 289-298. (SCI)
[26] B. Cheng, M. Liu (Corresponding author), Bolian Liu, Proof of a conjecture on the nullity of a connected graph in terms of order and maximum degree, Linear Algebra Appl., 587 (2020), 291-301. (SCI)
[27] M. Liu, H. Shan, X. Gu, Spectral characterization of the complete graph removing a path, Discrete Appl. Math., 284 (2020) 499–512. (SCI)
[28] M. Liu, K. Cheng, I. Tomescu, Some notes on the extremal k-generalized quasi-unicyclic graphs with respect to Zagreb indices, Discrete Appl. Math., 284 (2020) 616–621. (SCI)
[29] M. Liu, I. Tomescu, J. Liu, Unified extremal results for $k$-apex unicyclic graphs (trees), Discrete Appl. Math., 288 (2021), 35-49. (SCI)
[30] M. Liu, K. Cheng, B. Furtula, Minimum augmented Zagreb index of c-cyclic graphs, Discrete Appl. Math., 295 (2021) 32–38. (SCI)
[31] C. Chen, M. Liu (Corresponding author), X. Gu, K. C. Das, Extremal augmented Zagreb index of trees with given numbers of vertices and leaves, Discrete Math., 345 (2022) 112753. (SCI)
[32] M. Liu, X. Gu, Spectral strengthening of a theorem on transversal critical graphs, Discrete Math., 345 (2022) 112717. (SCI)
[33] M. Liu, B. Xu, On connected partition with degree constraints, Discrete Math., 345 (2022) 112680. (SCI)
[34] C. Chen, M. Liu (Corresponding author), X. Chen, W. Lin, On general ABC-type index of connected graphs, Discrete Appl. Math., 315 (2022) 27–35. (SCI)
[35] Y. Huang, M. Liu (Corresponding author), F. Belardo, The general spectral radii of (multicone-)graphs with prescribed degree sequence, Linear Multilinear Algebra, 70 (2022), 4751–4777. (SCI)
[36] P. Wei, M. Liu (Corresponding author), Note on Sombor index of connected graphs with given degree sequence, Discrete Appl. Math., 330 (2023) 51–55. (SCI)
[37] M. Liu, S. Pang, F. Belardo, A. Ali, The k-apex trees with minimum augmented Zagreb index, Discrete Math., 346 (2023) 113390. (SCI)
[38] M. Liu, C. Chen, S.-G. Guo, J. Peng, T. Chen, The Aα-spectral radius of dense graphs, Linear Multilinear Algebra, 71 (2023), 1044–1053. (SCI)
[39] P. Wei, M. Liu (Corresponding author), I. Gutman, On (exponential) bond incident degree indices of graphs, Discrete Appl. Math., 336 (2023) 141–147. (SCI)
[40] H. Shan, M. Liu, On the relationship between shortlex order and Aa-spectral radii of graphs with starlike branch tree, Discrete Math., 347 (2024) 113772. (SCI)
[41] J. Ye, M. Liu*, Z. Stani?, Two classes of graphs determined by the signless Laplacian spectrum, Linear Algebra Appl., 708 (2025) 159-172. (SCI)
(III) 更多的SCI論文：
[1] M. Liu, B. Liu, Degree series of the 3-harmonic graphs, Appl. Math. J. Chinese Univ. 23 (2008), 481-489
[2] B. Liu, Z. Chen, Liu M., On graphs with largest Laplacian index, Czechoslovak Math. J. 58(4) (2008), 949-960. (SCI)
[3] B. Liu, Liu M., Z. You, Erratum to "A note on the largest eigenvalue of non-regular graphs", Electronic J. Linear Algebra, 18 (2009), 64-68. (SCI)
[4] M. Liu, B. Liu, New sharp upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem., 62 (2009), 689-698. (SCI)
[5] Liu M., B. Liu, Trees with the seven smallest and fifteen greatest Hyper-Wiener indices, MATCH Commun. Math. Comput. Chem., 63 (2010), 151-170. (SCI)
[6] M. Liu, A note on D-Equienergetic graphs, MATCH Commun. Math. Comput. Chem., 64 (2010), 135-140. (SCI)
[7] M. Liu, A simple approach to order the first Zagreb indices of connected graphs, MATCH Commun. Math. Comput. Chem., 63 (2010), 425-432. (SCI)
[8] M. Liu, Bounds on the spectral radius of the line distance matrix, MATCH Commun. Math. Comput. Chem., 63 (2010), 717-724. (SCI)
[9] M. Liu, B. Liu, Some results on the Laplacian spectrum spectrum, Comput. Math. Appl., 59 (2010), 3612-3616. (SCI, EI)
[10] M. Liu, B. Liu, Q. Li, Erratum to The trees on vertices with the first to seventeenth greatest Wiener indices are chemical trees', MATCH Commun. Math. Comput. Chem., 64 (2010), 743-756. (SCI)
[11] M. Liu, X. Tan, B. Liu, The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices, Czechoslovak Math. J., 60(3) (2010), 849-867. (SCI)
[12] M. Liu, B. Liu, On the variable Wiener indices of trees with given maximum degree, Math. Comput. Modelling, 52 (2010), 1651-1659. (SCI, EI)
[13] M. Liu, B. Liu, On the Wiener polarity index, MATCH Commun. Math. Comput. Chem., 66 (2011), 293-304. (SCI)
[14] M. Liu, B. Liu, F. Wei, Graphs determined by its (signless) Laplacian spectra, Electronic J. Linear Algebra, 22 (2011), 112-124. (SCI)
[15] M. Liu, B. Liu, A note on sum of powers of the Laplacian eigenvalues of graphs, Appl. Math. Lett., 24 (2011), 249-252. (SCI)
[16] M. Liu, B. Liu, The second Zagreb indices and Wiener polarity indices of trees with given degree sequences, MATCH Commun. Math. Comput. Chem., 67 (2012), 439-450. (SCI)
[17] M. Liu, B. Liu, New method and new results on the order of spectral radius, Comput. Math. Appl., 63 (2012) 679-686. (SCI, EI)
[18] M. Liu, B. Liu, Some results on the majorization theorem of connected graphs, Acta Math. Sin., Eng. Ser., 28 (2012), 371-328. (SCI)
[19] M. Liu, B. Liu, Some results on the spectral radii of trees, unicyclic and bicyclic graphs, Electronic J. Linear Algebra, 23 (2012), 327-339. (SCI)
[20] M. Liu, Some graphs determined by their (signless) Laplacian spectra, Czechoslovak Math. J., 62(4) (2012), 1117-1134. (SCI)
[21] M. Liu, B. Liu, On sum of powers of the signless Laplacian eigenvalues of graphs, Hacet. J. Math. Stat., 41(4) (2012), 527-536. (SCI)
[22] M. Liu, The (signless) Laplacian spectrum of c-cyclic graphs with n vertices and k pendant vertices, Electronic J. Linear Algebra, 23 (2012), 942-952. (SCI)
[23] B. Liu, M. Liu, Z. You, The majorization theorem for signless Laplacian spectral radii of connected graphs, Graphs Combin., 29 (2013), 281-287. (SCI)
[24] M. Liu, F. Li, K. Ch. Das, Ordering the Zagreb coindices of connected graphs, MATCH Commun. Math. Comput. Chem., 70 (2013), 939-948. (SCI)
[25] M. Liu, B. Liu, A note on the LEL-equienergetic graphs, Ars Combin., 113 (2014), 435-439. (SCI)
[26] H. Li, Y. Liang, M. Liu, B. Xu, On minimum balanced bipartitions of triangle-free graphs, J. Comb. Optim. 27 (2014), 557-566. (SCI)
[27] M. Liu, B. Liu, X. Tan, The first nine maximal LEL-invariant of graphs with n vertices, Util. Math., 93 (2014), 153-160. (SCI)
[28] M. Liu, F. Wei, B. Liu, On the Laplacian spectral radii of tricyclic graphs, Ars Combin., 114 (2014), 129-143. (SCI)
[29] M. Liu, B. Liu, The nine smallest hyper-Wiener indices of trees and the eight smallest Wiener (hyper-Wiener) indices of unicyclic graphs, Util. Math., 95 (2014): 129-139. (SCI)
[30] M. Liu, B. Liu, On the signless Laplacian spectra of bicyclic and tricyclic graphs, Ars Combin., 120 (2015), 169-180. (SCI)
[31] I. Gutman, K. Xu, M. Liu, A congruence relation for Wiener and Szeged indices, Filomat, 29:5 (2015), 1081-1083. (SCI)
[32] M. Liu, B. Liu, R. Li, The strong pseudochromatic number of a graph, Util. Math., 98 (2015), 3-21. (SCI)
[33] M. Liu, B. Xu, On judicious partitions of graphs, J. Comb. Optim., 31 (2016), 1383-1398. (SCI)
[34] K. Ch. Das, M. Liu (Corresponding author), Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs, Czechoslovak Math. J., 66 (2016), 1039–1048. (SCI)
[35] K. Ch. Das, M. Liu, Kite graphs determined by their spectra, Applied Math. Comput., 297 (2017), 74-78. (SCI)
[36] K. Ch. Das, M. Liu (Corresponding author), Minimal extremal graphs for addition of algebraic connectivity and independence number of connected graphs, Filomat, 31 (2017), 5545-5551. (SCI)
[37] M. Liu, Y. Zhu, H. Shan, K. Ch. Das, Erratum to "The spectral characterization of butterfly-like graphs", Linear Algebra Appl., 539 (2018), 274-276. (SCI)
[38] M. Liu, K. Ch. Das, On the ordering of distance-based invariants of graphs, Appl. Math. Comput., 324 (2018), 191-201. (SCI)
[39] K. Ch. Das, M. Liu, On two conjectures of spectral graph theory, Bull. Iran. Math. Soc., 44 (2018), 43-51. (SCI)
[40] Y. Yao, M. Liu (Corresponding author), K. Ch. Das, Y. Ye, Some extremal results for vertex-degree-based invariants, MATCH Commun. Math. Comput. Chem., 81 (2019) 325-344. (SCI)
[41] Y. Yao, M. Liu, X. Gu, Unified extremal results for vertex--degree--based graph invariants with given diameter, MATCH Commun. Math. Comput. Chem., 82 (2019), 699-714. (SCI)
[42] M. Liu, Y. Yuan, K. Ch. Das, The fan graph is determined by its signless Laplacian spectrum, Czechoslovak Math. J., 70 (2020), 21-31. (SCI)
[43] M. Liu, Y. Yao, K. Ch. Das, Extremal results for cacti, Bull. Malays. Math. Sci. Soc., 43 (2020), 2783-2798. (SCI)
[44] M. Liu, G. Zhang, K. Ch. Das, Some properties of algebraic connectivity, Nation. Academy Sci. Lett., 43 (2020), 537–542. (SCI)
[45] M. Liu, Y. Wu, H.-J. Lai, Unified spectral Hamiltonian results of balanced bipartite graphs and complementary graphs, Graphs Combin., 36 (2020), 1363-1390. (SCI)
[46] X. Tan, M. Liu (Corresponding author), J. Liu, On the Maximal General ABC Index of Graphs with Fixed Maximum Degree, MATCH Commun. Math. Comput. Chem., 85 (2021), 121-130. (SCI)
[47] K. Cheng, M. Liu, Fr. Belardo, The minimal augmented Zagreb index of k-apex trees for k {1,2,3}, Appl. Math. Comput., 402 (2021), 126139. (SCI)
[48] M. Liu, K. C. Das, G. Zhang, The maximum number of spanning trees of a graph with given matching number, Bull. Malays. Math. Sci. Soc., 44 (2021) 3725–3732. (SCI)
[49] W. Zhou, S. Pang, M. Liu, A. Ali, On bond incident degree indices of connected graphs with fixed order and number of pendent vertices, MATCH Commun. Math. Comput. Chem., 88 (2022), 625–642. (SCI)
[50] Y. Lan, P. Wei, M. Liu, C. Chen, Maximum and minimum Lanzhou index of c-cyclic graphs, MATCH Commun. Math. Comput. Chem., 92 (2024) 671–688. (SCI)
[51] P. Wei, W. Jia, F. Belardo, M. Liu, Maximal Lanzhou index of trees and unicyclic graphs with prescribed diameter, Appl. Math. Comput., 488 (2025) 129116. (SCI)
(IV) 發表的SCI綜述：
[1] M. Liu, B. Liu, A survey on recent results of variable Wiener index, MATCH Commun. Math. Comput. Chem., 69 (2013), 491-520. (SCI)
[2] K. Xu, M. Liu, K. Ch. Das, I. Gutman, B. Furtula, A survey on graphs extremal with respect to distance-based topological indices, MATCH Commun. Math. Comput. Chem., 71 (2014), 461-508. (SCI)
[3] M. Liu, B. Liu, K. Ch. Das, Recent results on the majorization theory of graph spectrum and topological index theory-a survey, Electronic J. Linear Algebra, 30 (2015), 402-421. (SCI)
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