Professional Activities
1. Invited speaker, Complexity and algorithmic aspects of the Variant Domination Problems in Geometric Intersection Graphs, The symposium on Graph theory and Algorithms, Sep 24-25, 2022, Ningbo University, Ningbo, Zhejiang, China.
2. Invited speaker, On zero forcing number, Workshop on graph theory and Combinatorics, Sep 18-19, 2021, Northwestern Polytechnical University, Xi’an, Shanxi, China.
3. Invited speaker, Characterizations on graphs which achieve some upper bounds for their zero forcing number, Graph theory and Network Optimization, Nov. 6-7, 2021, Xi’an Jiaotong University, Xi’an, Shanxi, China.
4. Invited speaker, Complexity and characterizations of edge-related dominations on graphs, The 2021 Symposium on Graph Theory and Combinatorics, Jul 9-12, 2021, Minnan Normal University, Zhangzhou, Fujian, China.
5. Invited speaker, Algorithmic and complexity aspects of problems related to total restrained domination for graphs, The Symposium on Algebraic Graph Theory and Mathematical Optimization, Jul 3-5, 2021, Qinghai Normal University, Xining, Qinghai, China.
6. Invited speaker, Charaterizations for non-bicritical 3-(total) -dominationcritical graphs, The 2020 Symposium on graph theory, combinatorics and their applications of CSIAM, Dec 4-6, 2020, Sanya, Hainan, China.
7. Invited speaker, Matching-related properties of domination-critical graphs, The 18th Annual Meeting of China Industrial and Applied Mathematics Society, Oct 29-Nov 1, 2020, Changsha, Hunan, China.
8. Invited speaker, Independent perfect domination sets in Semi-Cayley graphs, AAIM 2020, Aug 10-12, 2020, Online.
9. Invited speaker, Recent study on total edge domination and bicriticality of vertex-domination-critical graphs, the Ninth National Conference on Graphs and Combinatorics, Aug 15-17, 2020, Online.
10. Invited speaker, The characterizations of edge-related domination of graphs, The symposium on Combinatorics and Graph theory, Aug 14, 2020, Nankai University, Tianjin, China.
11. Invited speaker, Bicritical properties in connected domination critical graphs, The 2020 workshop on graph theory and its application, Jan 10-11, 2020, Qinghai Normal University, Xining, Qinghai, China.
12. Invited speaker, Bicritical properties in connected domination critical graphs, Workshop on graph theory and its applications, Dec 20-23, 2019, Minnan Normal University, Zhangzhou, Fujian, China.
13. Invited speaker, 2-rainbow edge and Roman 2-edge domination numbers on trees, The Hehui third symposium on Graph theory and Combinatorics, Dec 6-8, 2019, Anhui University, Hehui, Anhui, China
14. Invited speaker, Study on certain edge dominations and some related results on trees, The sixth workshop on graph theory and combnatorial optimization, Oct 25-27, 2019, Nankai University, Tianjin, China.
15. Invited speaker, The complexity of total edge domination and some related result on trees, 2019 International Conference on colored graphs, bigdata and interconnection networks, July 19-21, 2019, Qinghai Normal University, Xining, Qinghai, China.
16. Invited speaker, April 19-21, 2019, Taizhou University, Taizhou, Jiangsu, China.
17. Invited speaker, The complexity of total edge domination and some related results on trees, Graph theory and its applications symposium of UESTC, Nov. 22-23, 2018, Chengdu, Sichuan, China.
18. Invited speaker, On the maximum value of the eccentric distance sums of cubic transitive graphs, 2018 Workshop on graph theory and its applications, Oct. 12-14, 2018, Shandong University of Technology, Zibo,Shandong, China.
19. Invited speaker, Roman {k}-domination in trees and complexity results for some classes of graphs, The third international symposium on the frontier of graph theory, Apr. 24-25, 2018, Qinghai Normal University, Xining, Qinghai, China.
20. Invited speaker, Compact Phylogenetic trees, The forth symposium on graph theory and combinatorial optimization, Oct. 6-10, 2017, Nankai University, Tianjin, China.
21. Invited speaker, Average distances in graphs, the Seventh National Conference on Graphs and Combinatorics, Aug. 14-17, 2016, Hebei Normal University, Hebei Province, China.
22. Invited speaker, The complete forcing numbers of graphs, 12th Annual Meeting of the International Academy of Mathematical Chemistry & 2016 International Conference on Mathematical Chemistry, July 4-8, Nankai University, Tianjin, China.
23. Invited speaker, The complete forcing numbers of graphs, Twelfth National Congress and the 80 annual meeting of the National Association for Mathematics, Nov. 21-24, 2015 Capital Normal University, Beijing, China.
24. Invited speaker, MAD clique trees, Symposium on Graphs, Supergraphs and applications, Dec. 12-13, 2015, Center for graphs, combinatorics and networks, Beijing, China.
25. Invited speaker, The complete forcing numbers of graphs, 2015 international Conference on Graph Theory and Combinatorics & Eighth Crossstrait Conference on Graph theory and Combtinatorics, Jun. 26-30, 2015, National Sun Yat-sen University, Kaohsiung, Taiwan.
26. Contributed speaker, The complete forcing number of graphs, the Sixth National Conference on Graphs and Combinatorics, Nov 7-10, 2014, South China Normal University, Guangzhou, Guangdong Province.
27. Invited speaker, The end-vertex problem for graph searching algorithms, Jun. 6, 2014, Shanghai Jiao Tong University, Shanghai.
28. Contributed speaker, Moplex elimination orderings generated by the LexDFS algorithm, 2012 International Conference on Graph Theory, Combinatorics and Applications, Oct. 26-30, 2012, Zhejiang Normal University, Jinhua, Zhengjiang Province.
29. Contributed speaker, Minimum average distance clique trees, the Fifth National Conference on Graphs and Combinatorics, Jul. 16-18, 2012, Luoyang Normal University, Luoyang, Henan Province.
30. Contributed speaker, Multiple Resolution Community Structure Analysis, the Tenth International Symposim, ISORA 2011, Aug. 28-31, 2011, Dunhuang, Gansu Province, China.
31. Contributed speaker, The Hosoya polynomial decompositions for catacondensed benzenoid graphs, the Third National Conference on Graphs and Combinatorics, Jul. 20-23, 2008, East China Normal University, Shanghai.

Teaching experience
1. Undergraduate Course:
• Introduction to Graph theory
• Introduction to Algorithms
• Combinatorics
• Analytical Geometry
• Operations Research
• Linear algebra
• Advanced mathematics
• Calculus
• · · · · · ·
2. Graduate Course:
• Graph Theory
• Combinatorics
• Combinatorial Optimization
• Approximation algorithms
• Algorithmic Graph Theory and Perfect Graph
• Hypergraph
• Fundamentals of domination in graphs
• Random graphs
• · · · · · ·
Research Team
1. Students:
• Doctoral candidates:
Xiao-Yun Lv(2022), Lina Wei(2022), Jie Chen(2021), Cai-Xia Wang (2020), Yu Yang(2019), Yi-Ping Liang(2018), Xiao-Meng Wang(2018), Yong-De Feng(2018), Yan-Ting Xie(2018).
• Academic Master candidates:
Lina Tang(2022), Xing-Qi Guo(2022), Zong-Ze Xing(2022), ZhiXuan Luo (2022), Xiao-Fei Sun(2021), Bin Sun(2021), Rui-Meng Miao(2021), Yu Li(2020), Jin-Hui Li(2020), Wan-Li Zuo(2020), CongHui Zhao(2020), Tian-Xia Jia(2020).
• Professional Master candidates (Applied Statistics):
Xin-Lin Zhang(2022), Yun-Jie Feng(2022), Jian-Min Jiao(2022), NaNa Yu(2022), Wen-Xuan Xiao(2022), Shi-Bo Wei(2021), Tao Xiao(2021), Yu-Jie Cao(2021), Fan Zhang(2021), Fu-Rong Yang(2021), Qing-Rong Yun(2020), Wen-Li Sang(2020), Peng-Bo Li(2020), Yong Liang(2020).
2. Graduated:
• PhD Degree:
Xiao-Lu Gao (2022.6), Zhuo Pan (2021.12).
• Academic Master:
Qi Lu(2022), Bing-Xue Fu(2022), Peng Pan(2022), Jie Chen(2021), Tao Wang(2021), Gui-Qiang Mou(2021), Lu-Yao Yang(2020), YuLan Hu(2020), Meng-Ke Liu(2020), Yu Yang(2019), Cai-Xia Wang (2019), Hong-Juan Wang(2019), Shan-Shan Xie(2018), Qing-Hong Wang(2018), Xiao-Lu Gao(2017), Ju Qiao(2017), Yi-Fang Xu(2015), Song-Xiu Liu(2015(National Scholarship winner in 2013)), QingHua He(2015), Zhuan-Zhuan Zhang(2014), Hai-Yang Chen(2013).
• Professional Master (Applied Statistics):
Dan-Dan Wu(2022), Bian-Xia Wang(2022), Xiao-Yu Zhu(2022), XiaoQian Chen(2022), Jing-Yu Zhang(2022), Rong Zhu(2021), Xiao-Dan Jia(2021), Lu Bai(2021), Xu-Chun Zhang(2021), Yu-Ling Yang(2021), Jun-Ji Lai(2020), Fei-Yan Liu(2020), Rui-Jia Li(2020), Miao Peng (2020), Yi-Fei Wang(2020), Cheng Zhu(2019), Yan-Wen Wang(2019), Xiao-Qian Li(2018), Bo-Qing Lv(2018), Ya-Feng Wang(2017), JianHnag Tang(2016), Shuai-Feng Shao(2016), Qiu-Xia Zhang(2015 (National Scholarship winner in 2014)).

• 2021.1 ∼ 2024.12
Studies on Murty-Simon conjecture, properties of (total) domination and edge domination-parameter critical graphs, Principal Investigator, General Program, Grant No. 12071194, National Natural Science Foundation of China (NSFC)
• 2016.1 ∼ 2019.12
Studies on average distances of graphs and related problems, Principal Investigator, General Program, Grant No. 11571155, National Natural Science Foundation of China (NSFC)
• 2014.1 ∼ 2017.12
Studies on machting forcing and matching preclusion problems of graphs, Joint member, General program, Grant No. 11371180, National Natural Science Foundation of China (NSFC)
• 2011.1 ∼ 2013.12
Research on based-distance topological indices and Hosoya polynomials, Principal Investigator, Youth Research Grant, Grant No. 11001113, National Natural Science Foundation of China (NSFC)
• 2009.1 ∼ 2009.12
Research on problems about Hosoya polynomials of graphs, Principal Investigator, TianYuan special funds for Mathematics, Grant No. 10826075, National Natural Science Foundation of China (NSFC)
• 2010.1 ∼ 2010.12
Research on problems about evaluating functions for community structures in complex networks, Principal Investigator, Grant No. lzujbky-2009-51, the Fundamental Research Funds for the Central Universities
• 2008.6 ∼ 2010.7
Research on properties and algorithms about Wiener indices and Hosoya polynomials of graphs, Principal Investigator, Grant No. 20080440071, China Postdoctoral Science Foundation (CPSF)

1. Yan-Ting Xie, Yong-De Feng, *Shou-Jun Xu, Characterization of 2-arc-transitive partial cubes, Discrete Math., Accepted.
2. Yan-Ting Xie, Yong-De Feng, *Shou-Jun Xu, Hypercube embeddings and Cayley graphs generated by transpositions, Mathematics, 10 (2022) 1575 (https://doi.org/10.3390/math10091575).
3. Yongde Feng, Yan-Ting Xie, Fengxia Liu, *Shou-Jun Xu, The Extendability of Cayley Graphs Generated by Transposition Trees, Math. Meth. Appl. Sci., 45 (2022) 7227-7237 (https:// doi.org/ 10.1002/ mma.8233).
4. Hong Chang, Yong-De Feng, Hong Bian, *Shou-Jun Xu, Complete forcing numbers of rectangular polynominoes, Acta mathematica Spalatensia, 1 (2021) 87-96.
5. Cai-Xia Wang, Yu Yang, Hong-Juan Wang, *Shou-Jun Xu, Roman k-domination in trees and complexity results for some classes of graphs, J. Combin. Optim. 42 (2021) 174-186.
6. Xiaomeng Wang, *Shou-Jun Xu, Xianyue Li, Independent perfect dominating sets in semi-Cayley graphs, Theor. Comput. Sci. 864 (2021) 50-57.
7. Jie Chen, *Shou-Jun Xu, A characterization of 3-γ-critical graphs which are not bicritical, Inform. Process. Lett. 166 (2021) 106062.
8. Xiao-Lu Gao, *Shou-Jun Xu, The LexCycle on P2 ∪ P3-free cocomparability graphs, Discrete Mathematics and Theoretical Computer Science (DMTCS) 22(4) (2020) #13.
9. Zhuo Pan, Xianyue Li, *Shou-Jun Xu, Complexity and characterization aspects of edge-related domination for graphs, J. Combin. Optim. 40 (2020) 757-773.
10. Zhuo Pan, Yu Yang, Xianyue Li, *Shou-Jun Xu, The complexity of total edge domination and some related results on trees, J. Combin. Optim. 40 (2020) 571-589.
11. Guangfu Wang, Yujun Yang, Yuliang Cao, Shou-Jun Xu, Unicyclic Graphs with the fourth extremal Wiener indices, J. of Chimistry 2020 ID: 2878901.
12. *Lianying Miao, Jingru Pang, Shou-Jun Xu, On the extremal values of the eccentric distance sum of trees with a given maximum degree, Discrete Appl. Math. 284 (2020) 375-383.
13. *Xiaomeng Wang, Shou-Jun Xu, Xing Gao, A Hopf algebra on subgraphs of a graph, J. Algebra and its Appl. (2020) 2050164.
14. Yan-Ting Xie, *Shou-Jun Xu, On the maximum value of the eccentric distance sums of cubic transitive graphs, Appl. Math.Comput. 359 (2019) 194-201.
15. Xiao-Lu Gao, *Shou-Jun Xu, Average distance, connected hub number and connected domination number, MATCH-Commun.Math. Comp. Chem. 82(1) (2019) 57-75.
16. *Zepeng Li, Zehui Shao, Shou-Jun Xu, 2-rainbow domination stability of graphs, J. Combin. Optim., 38 (2019) 836-845.
17. Wai Hong Chan, *Shou-Jun Xu, Note on the upper bound on mean distance in terms of minimum degree, Ars Comb. 143 (2019) 165-172.
18. Damir Vukiˇcevi´c, Shuang Zhao, *Jelena Sedlar, Shou-Jun Xu, Tomislav Doˇsli´c, Global forcing number for maximal matchings, Discrete Math. 341 (2018)801-809.
19. Qing-Hua He, *Shou-Jun Xu, Hosoya polynomials of random phenylene chains, Ars Comb. 141 (2018) 259-268.
20. Yan-Ting Xie, *Shou-Jun Xu, Nested Unimodality, AUSTRALAS. J. COMBIN., 69 (1) (2017), 119-129.
21. Shou-Jun Xu, Xiu-Song Liu, Wai Hong Chan, *Heping Zhang, Complete forcing numbers of primitive coronoids, J. Combin. Optim., 32(1) (2016) 318-330.
22. *Shou-Jun Xu, Qing-Hua He, Shan Zhou, Wai Hong Chan, Hosoya Polynomials of Random Benzenoid Chains, Iran. J. Math. Chem.(IJMC), 7(1) (2016) 29-38.
23. *Shou-Jun Xu, Rob Gysel, Dan Gusfield, Minimum average distance clique trees, SIAM J. Discrete Math. 29(3) (2015) 1706-1734.
24. *Wai Hong Chan, Shou-Jun Xu, Ge Nong, A linear-time algorithm for computing the complete forcing number and the Clar number of catacondensed hexagonal systems, MATCH-Commun. Math. Comp. Chem. 74(1) (2015) 201-216.
25. *Shou-Jun Xu, Heping Zhang, Jinzhuan Cai, Complete forcing numbers of catacondensed hexagonal systems, J. Combin. Optim., 29(4) (2015) 803-814.
26. Qiu-Hua He, *Shou-Jun Xu, Schultz polynomial and modified Schultz polynomial of a random benzenoid chain, Ars Comb., 120 (2015) 39-50.
27. Qiu-Xia Zhang, *Shou-Jun Xu, Hai-Yang Chen, The Hosoya polynomial of one-pentagonal carbon nanocone, Fuller. Nanotub. Car.N. 22 (2014) 866-873.
28. *Shou-Jun Xu, Hai-Yang Chen, Qiu-Xia Zhang, Liangping Tu, Hosoya polynomials of twisted toroidal polyhexes, Ars Comb. 114 (2014) 417-425.
29. Xiu-Song Liu, *Shou-Jun Xu, Liangping Tu, Global forcing numbers of Handgun-shaped benzenoid systems, Curr. Nanoscience, 10 (2014) 766-771.
30. Qing-Hua He, Jian-Zhong Gu, *Shou-Jun Xu, Wai Hong Chan, Hosoya Polynomials of Hexagonal Triangles and Trapeziums, MATCHCommun. Math. Comp. Chem., 72(3)(2014) 835-843.
31. Qiu-Xia Zhang, *Shou-Jun Xu, Hai-Yang Chen, The Hosoya polynomial of one-quadrilateral carbon nanocone, Optoelectron. Adv. Mat. 7(2013) 770-775.
32. Xiaoxia Lin, *Shou-Jun Xu, Yeong-Nan Yeh, Hosoya polynomials of Circumcoronene Series, MATCH-Commun. Math. Comp. Chem.69(3) (2013) 755-763.
33. *Shou-Jun Xu, Xianyue Li, Ronghua Liang, Moplex elimination orderings generated by the LexDFS algorithm, Discrete Appl. Math. 161(13-14) (2013) 2189-2195.
34. *Shou-Jun Xu, Qiu-Xia Zhang, The Hosoya Polynomial of OneHeptagonal Nanocone, Curr. Nanoscience 9(3) (2013) 411-414.
35. Shou-Jun Xu, Jiguang Wang, Junhua Zhang, *Xiang-Sun Zhang, Multiple resolution community structure analysis, IEEE international conference on computational systems biology, The tenth InternationalSymposium on Operations Research and Its Applications (ISORA 2011),334-349.
36. Jianfu Chen, Shou-Jun Xu, *Heping Zhang, Hosoya polynomials of TUC4C8(R) nanotubes, Int. J. Quantum Chem., 109(4) (2009) 641-649.
37. Shou-Jun Xu, *Heping Zhang, Hosoya polynomials of TUC4C8 (S) nanotubes, J. Math. Chem., 45(2) (2009) 488-502.
38. *Heping Zhang, Shou-Jun Xu, None of coronoid systems can be isometrically embedded into a hypercube, Discrete Appl. Math., 156(14) (2008) 2817-2822.
39. Shou-Jun Xu, *Heping Zhang, The Hosoya polynomial decomposition for catacondensed benzenoid graphs, Discrete Appl. Math.,156(15) (2008) 2930-2938.
40. Shou-Jun Xu, *Heping Zhang, The Hosoya polynomial decomposition for hexagonal chains, Mathematical and Computer Modelling, 48(3-4) (2008) 601-609.
41. Shou-Jun Xu, *Heping Zhang, Generalized Hosoya polynomials of hexagonal chains, J. Math. Chem., 43(2) (2008) 852-863.
42. Shou-Jun Xu, *Heping Zhang, Hosoya polynomials under gated amalgamations, Discrete Appl. Math., 156(12) (2008) 2407-2419.
43. Shou-Jun Xu, *Heping Zhang, M.V. Diudea, Hosoya polynomials of zig-zag open-ended nanotubes, MATCH-Commun. Math. Comput. Chem., 57 (2007) 443-456.
44. Shou-Jun Xu, *Heping Zhang, Hosoya polynomials of armchair open-ended nanotubes, Int. J. Quantum Chem., 107 (2007) 586-596.
45. *Heping Zhang, Shou-Jun Xu, Yujun Yang, Wiener index of toroidal polyhexes, MATCH-Commun. Math. Comput. Chem., 6 (2006) 153-168;

1. 2012, Third Prize of Natural Science Award in Gansu Province.
2. 2013, Younger Teacher Talent award of Gansu College.
3. 2015, LONGJI teaching core award of Lanzhou University.
4. 2015, Advisor for one national first prize in CUMCM (China Undergraduate Mathematical Contest in Modeling)
5. 2019, Moral standard teacher of Lanzhou University.
6. 2021, Excellent advisor for master’s thesis of Gansu Province, China