Academic Positions 

• Assistant Professor, Indian Institute of Technology (BHU) Varanasi, since December 2016.
• Visiting Researcher, University of Waterloo, Canada, Summer 2019.
• Research Assistant Professor, SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu, India, during 2013-2016.   

Research

• Post Doctoral Fellow, Institute of Mathematical Sciences(IMSc), Chennai, 2012–2013.
• Research Associate, Institute of Bioinformatics and Translational Research, UMIT - The Health and Life Sciences University, Austria, 2010–2011.
• NBHM Post Doctoral Fellow, Institute of Mathematical Sciences(IMSc), Chennai, 2009–2010.
• Visiting Research Fellow, University of Oklahoma, Norman, USA, 2009.

Education

• Ph.D. Mathematics, Department of Mathematics, Indian Institute of Technology Madras, India.
  • Thesis Title: Optimal Embedding of Trees in Interconnection Networks 
• M.Sc. Mathematics, Department of Mathematics, Indian Institute of Technology Madras, India.
  • Dissertation On: A Study of Public Key Cryptosystems
• B.Sc. Mathematics, JBAS (SIET) Womens’ College, University of Madras, Chennai.  

​Courses Currently Teaching (Odd Semester 2021-2022):

• MA 551: Mathematics (PG Level Course) 
•  

Courses Currently Teaching (Even Semester 2021-2022):

• MA 102: Engineering Mathematics-II
• CSO 322: Theory of Computation 

Courses Teaching/Taught(several times) at IIT(BHU) : 

• MA 101: Engineering Mathematics-I
• MA 102: Engineering Mathematics - II 
• CSO 204N: Discrete Mathematics(Odd  Semesters)
• CSO 322: Theory of Computation(Even Semesters)
• Universal Human Values - I
• Universal Human Values - II 
• Universal Human Values for Ph.D. Students 
• MA 551: Mathematics (PG Level Course)

Courses Taught at SRM University:

• Advanced Graph Theory (Ph.D. Level Course)
• Discrete Mathematics (UG Level Course)
• Data Structures and Algorithms (M.Sc. Course)
• Probability Theory and Mathematical Statistics (M.Sc. Course)
• Boolean Algebra (M.Sc. Course, redesigned by me)
• Algebra (M.Sc. Course)
• Functional Analysis (M.Sc. Course)
• Complex Analysis (M.Sc. Course)

1. Principle Investigator for the Funded Research Project (MATRICS) titled: Applications of Spectral Graph Theory in analyzing the structural properties of large scale networks, SERB, INDIA, March 2019 - June 2022 (Ongoing).  
2. Principal Investigator for Seed Grant from IIT(BHU), Varanasi:   
   • Amount of Grant:  Rs. 4,20,000/- 
   • Duration: August 2017-March 2018.  
3. Principle Investigator for the Funded Research Project titled: A Different Perspective of Spectral Graph Theory in the Structural Characterization of Networks, SERB, INDIA. 
   • Amount of Grant: Rs. 14,04,000/-
   • Duration: August 2014 - February 2018.

Publications:

• Abhay Rajpoot and Lavanya Selvaganesh,  Potential Application of Novel AL indices as Molecular Descriptors, Journal of Molecular Graphics and Modelling, 118, 1-10, 2023, 108353. https://doi.org/10.1016/j.jmgm.2022.108353  
• Abhay Rajpoot and Lavanya Selvaganesh,  Supplementary Data for Potential Application of Novel AL indices as Molecular Descriptors, Journal of Molecular Graphics and Modelling, 118, 1-10 and 1-7, 2023, 108353. https://ars.els-cdn.com/content/image/1-s2.0-S1093326322002327-mmc1.pdf
• Arunkumar, G., Peter Cameron, Rajat Kanti Nath, and Lavanya Selvaganesh, Super Graphs on Groups - I, Graphs and Combinatorics, 38, 100 2022. https://doi.org/10.1007/s00373-022-02496-w
• Ajay Kumar, Lavanya Selvaganesh, T Tamizh Chelvam, Connectivity of Superpower Graphs of some non-Abelian finite groups, Discrete Mathematics, Algorithms and Applications (DMAA), Accepted, 2022.https://doi.org/10.1142/S1793830922501087 
• Abhay Rajpoot and Lavanya Selvaganesh, Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching, Iranian Journal of Mathematical Chemistry, 13(2):145-165, 2022. https://doi.org/10.22052/IJMC.2022.243396.1605
• Abhay Rajpoot and Lavanya Selvaganesh, Bounds and Extremal graphs of Second Reformulated Index For Graphs With Cyclomatic Number At Most Three, Kuwait Journal of Science, 49(1): 1-21, 2022. https://doi.org/10.48129/kjs.v49i1.10447.
• Ajay Kumar Patel, Lavanya Selvaganesh, Sanjay Kumar Pandey, Energy and Inertia of the Eccentricity Matrix of Coalescence of Graphs, Discrete Mathematics, 344(12), 2021, 112591. https://doi.org/10.1016/j.disc.2021.112591
• Ajay Kumar, Lavanya Selvaganesh, Peter Cameron and T Tamizh Chelvam,  Recent developments on the power graph of finite groups - A survey, AKCE International Journal of Graphs and Combinatorics,  18:2, 65-94, 2021. https://doi.org/10.1080/09728600.2021.1953359
• Sivakumar Karunakaran and Lavanya Selvaganesh, A unique and novel graph matrix for efficient extraction of structural information of networks, Electronic Journal of Graph Theory and Applications 9 (1), 39–51, 2021. 
• Abhay Rajpoot and Lavanya Selvaganesh, Extension of M-Polynomial and Degree Based Topological Indices for Nanotube, TWMS J. App. and Eng. Math. 11:Special Issue, 268-279, 2021. http://jaem.isikun.edu.tr/web/index.php/archive/109-vol11-special-issue/656-extension-of-m-polynomial-and-degree-based-topological-indices-for-nanotube 
• Abhay Rajpoot and Lavanya Selvaganesh, Bounds of the Symmetric Division Deg Index For Trees And Unicyclic Graphs With A Perfect Matching, Iranian J. Math Chem., 11:3, 141-159, 2020.  doi: 10.22052/IJMC.2020.214829.1481   
• Sivakumar Karunakaran and Lavanya Selvaganesh, A Novel Graph Matrix Representation: Sequence of Neighbourhood matrices with an application, SN Appl. Sci. 2, 944,  2020. doi:10.1007/s42452-020-2635-1
• S. Lavanya, B. Jayaram, S. Arumugam and K. Thulasiraman, Virtual Topologies for Topology Abstraction Service for IP-VPNs, 17th International Telecommunications Network Strategy and Planning Symposium (NETWORKS 2016), Montreal, QC, IEEE Conference Proceedings, 2016, pp.213-220. doi: 10.1109/NETWKS.2016.7751178.   

• Dehmer M., Lavanya Sivakumar and Varmuza K, Uniquely Discriminating Molecular Structures Using Novel Eigenvalue-Based Descriptors, MATCH Commun. Math. Comput. Chem., 67:1, 147-172, 2012.
• Dehmer M and Lavanya Sivakumar,  Recent Developments in Quantitative Graph Theory: Information Inequalities for Networks, PLoS ONE 7(2): e31395, 2012. doi: 10.1371/journal.pone.0031395  
• Dehmer M and Lavanya Sivakumar, Towards Information Inequalities and Generalized Graph Entropies, PLoS ONE 7(2): e38159, 2012. doi: 10.1371/journal.pone.0038159 
• Dehmer M., Lavanya Sivakumar and Varmuza K, On Distance-Based Entropy Measures. In: Gutman I., Furtula B. (Eds): Distance in Molecular Graphs, Mathematical Chemistry Monographs 12, 123-138, 2011. http://www.pmf.kg.ac.rs/match/contentMCM12.html  
• S. Lavanya and S.A. Choudum, Embedding a Subclass of Trees into Hypercubes, Discrete Mathematics, 311, 866-871, 2011. http://dx.doi.org/10.1016/j.disc.2011.02.011 
• S. Lavanya, S.A.Choudum and V. Sunitha, Disjoint Paths in Hypercubes with Prescribed Origins and Lengths, International Journal of Computer Mathematics, 87:8,1692-1708, 2010. http://dx.doi.org/10.1080/00207160802566805
• S.A.Choudum, S. Lavanya and V. Sunitha, Embedding Double Starlike Trees Into Hypercubes, International Journal of Computer Mathematics, 88:1, 1-5, 2011. Available online at: http://dx.doi.org/10.1080/00207160903406554 
• S. Lavanya and S.A. Choudum, Complete k-ary trees and Hamming graphs, Australasian Journal of Combinatorics, 45, 15-24, 2009. http://ajc.maths.uq.edu.au/?page=get volumes&volume=45
• S. Lavanya and S.A. Choudum, Embedding Complete Ternary Trees Into Hypercubes, Discussiones Mathematicae Graph Theory, 28(3), 463-476, 2008. http://dx.doi.org/10.7151/dmgt.1420 

 Published as Book Chapters:

• Dehmer, M., Sivakumar, L. (2015). On Comparability Graphs: Theory and Applications. In Advances in Mathematical Chemistry and Applications: Revised Edition (Vol. 1, pp. 139–160). Elsevier Inc. https://doi.org/10.1016/B978-1-68108-198-4.50007-2
• Dehmer M, Lavanya Sivakumar, On Comparability Graphs: Theory and Applications, In Advances in Mathematical Chemistry and Applications, Vol 1, 2014, 21 pages. 
• S.A. Choudum, S. Lavanya, V. Sunitha, Introduction to Interconnection Networks, In   Handbook of Graph Theory, Combinatorial Optimization and Algorithms, Eds. K. Thulasiraman, T. Nishizeki, S. Arumugam, and A.Brandstädt, CRC Press, Taylor and Francis Group, 2015. 
• S. Lakshmivarahan, S. Lavanya, S.K. Dhall, Cayley Graphs, In Handbook of Graph Theory, Combinatorial Optimization and Algorithms, Eds. K. Thulasiraman, T. Nishizeki, S. Arumugam, and A.Brandstädt, CRC Press, Taylor and Francis Group, 2015. 
• S.A. Choudum, S. Lavanya, V. Sunitha, Graph Embedding and Interconnection Networks, In Handbook of Graph Theory, Combinatorial Optimization and Algorithms, Eds. K. Thulasiraman, T. Nishizeki, S. Arumugam, and A.Brandstädt, CRC Press, Taylor and Francis Group, 2015. 

Ph.D. (As Supervisor): 

• Mr. Abhay Rajpoot, UGC JRF, Ongoing.
• Mr. Ajay Kumar, UGC JRF, Ongoing.  
• Ms. Jesmina Pervin, CSIR JRF, Ongoing
• Ms. Smrati Pandey, Ongoing.  
• Mr. Shiva Prakasha, Ongoing. 

Ph.D. (as Co-Supervisor): 

• Mr. Ajay Kumar Patel (as Co-Supervisor), Ongoing. 

PG Project Supervision:

• Ms. Ruchika Modi: Refining Social Graph Connectivity by Network Augmentation, 2018. 
• Mr. K. Naveen Kumar: Optimizing information propagation across multiple social networks, 2018. 
• Mr. Sourav, Ensemble Predictive Modeling:  An implementation on the real world dataset and a review, 2019
• Ms. Swetha Rayala, Community Detection in networks: An implementation of modularity maximization technique, 2019.  
• Mr. Hitesh Kumar, Image Deblur Techniques for Image Sensitivity and Captioning, 2020.
• Mr. Akash Kumar Gupta, Efficient Influence Maximization in Social Networks, 2021. 
• Mr. Jogi Miglani, Positive/Negative Influence Maximization In Signed Networks, 2022. 
• Mr. Shourrya Srivastava, A PID based dynamic programming algorithm to calculate the treewidth, 2022. 

UG Project Supervision:

• Mr. Sourav, Machine learning and its applications to Networks, 2017 
• Mr. Hitesh Kumar, Automatic Image Captioning using Deep Learning techniques, 2018
• Mr. Akash Kumar Gupta, Efficient Influence Maximization in Social Networks, 2019. 
• Mr. Jogi Miglani, Positive Influence Maximization In Signed Networks, Stream Project, 2020. 
• Mr. Shourrya Srivastava, Tree Width and related algorithms, Stream Project, 2020. 
• Ms. Vishaka Tomar, Graph Applications in Image Processing, 2021.
• Mr. Mayank Singh, Stream Project, Ongoing. 
• Mr. Adarsh Mishra, Ongoing. 
• Ms. Velidamalli Sai Preetika, Ongoing.  

Exploratory Project Guidance: 

• 2021-22: Mr. Gandharv Jain, Ms. Kanishka Gour, Ms. Komal Vadodaria. 
• 2020-21: Mr. Anshu Kumar Jha, Mr. Deepanshu, Ms. Masetty Gayathri.
• 2019-20: Ms. Dhriti Singh, Ms. Eshwita Sai, Ms. Vishaka Tomar. 
• 2018-19: Ms. Mitisha Pandey, Mr. Shourrya Srivastava, Mr. Yash Gupta.  
• 2017-18: Mr. Pranshu Prakash Vaish,  Mr. Akash Kumar Gupta. 

Summer Intern Supervision:

• 2017: Ayush Ranjan Lohani, Undergraduate Student, Department Of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur 

Awards and Fellowships:

• Post-doctoral fellowship from National Board of Higher Mathematics, Department of Atomic Energy, India, 2009.
• Senior research fellowship from the Council of Scientific and Industrial Research, India, 2008.
• Secured All-India Rank 10 with a percentile score of 99.26 in "GATE 2003".
• Merit Scholarship during M.Sc. from Indian Institute of Technology Madras, India, 2001 - 2003.
• First Prize in Inter-Collegiate Math Olympiad at Stella Maris College, Chennai, India, 2001.

Memberships: 

• Life Member, Academy of Discrete Mathematics and Applications, India.
• Life Member, Indian Mathematical Society.
• Life Member, Ramanujan Mathematical Society.
• Life Member, Indian Science Congress Association
• Life Member, European Society of Mathematical Chemistry.
• Member, American Mathematical Society.
• Member, European Mathematical Society.
• Member, Society for Industrial and Applied Mathematics
• Member, International Linear Algebra Society 

 Guest Lectures/Invited Talk: 

• Keynote Lecture on " Potential Application of Novel AL indices as Molecular Descriptors", 8th Indo-US Workshop on Mathematical Chemistry, Virtual mode,  Sep 13-17, 2022. 
• Invited Talk on "Power Graphs from Groups", International Workshop in Graphs from Algebraic Structures, Manonmaniam Sundaranar University, Tirunelveli, Tamilnadu, India, October 07-09, 2021.  
• Invited Talk on "Spectral Properties of Eccentricity matrix", International Conference on Recent Trends in Modern Mathematics (RTMM-2021), St. John College Palayamkottai, Tamilnadu, India, September 23-24, 2021. 
• Invited Talk on "Spectral Properties of Eccentricity matrix for special classes of graphs" at Algebraic Graph Theory Seminar, University of Waterloo, Canada, August 16, 2021. 
• Contributed Talk on "Some Recent Results on Superpower Graph of Groups", Research Discussion on Groups and Graphs, Cochin University of Science and Technology, Kerala, India, 14 July 2021.  
• Contributed Talk on "Bounds Of The Symmetric Division Deg Index For Graphs With Cyclomatic Number At Most 2 and With A Perfect Matching" at the Minisymposium in Chemical Graph Theory, CanaDAM 2021, May 25-28, 2021. 
• Invited Talk on "Role of Algebraic Graph Theory in Network Engineering and Network Sciences", at the Workshop on "An Insight into Mathematical Modelling in Information and Communication Engineering, Department of Computer Science, SSN College of Engineering, Chennai, India, March 26-27, 2021.
• Invited talk on “Resistance Networks and Topological Indices”, at Virtual International Conference on Discrete Mathematics (ICDM-2020), University of Mangalore, Karnataka, India, February 8-10, 2021.
• Invited Talk on "Dominator Sequences in Hypercubes and the Forcing Set Conjecture " at the One Day International Webinar on Graph Theory organized by Department of Mathematics, Thiyagaraja College of Engineering, Madurai, August 19, 2020. 
• Invited Talk on "A short Survey on Power Graphs and Superpower graphs"  at the ​International Conference on Graph Connections, Bishop Chulaparambil Memorial College, Kottayam, INDIA, 06-08 August, 2020
• Invited Talk on "Statistical Methods for Machine learning" at the One-day National Level webinar on Mathematics in Machine Learning organized by Department of Mathematics, SSN College of Engineering, Chennai, India May 20, 2020. 
• Invited Talk on “A novel and efficient structural descriptor to test graph isomorphism” at the Banaras Hindu University Mathematical Society Conference on Emerging Trends in Combinatorics and its Applications, BHU Varanasi, India February 22 - 23, 2019. 
• Invited talk on “A novel and efficient structural descriptor to measure graph similarity”, at the International Conference on Graph Theory (ICGTA 2019) held at Amrita University, Coimbatore, India, January 4 - 6, 2019.
• Invited Talk on “Refining Social Network Connectivity via Network Augmentation”, at the International Conference on Discrete Mathematics and Network Sciences (ICDMANS 2018) held at BITS Pilani, Goa Campus, India, July 7 – 10, 2018.  
• Series of 10 lectures on “Spectral Graph Theory and its applications” at the ACM-India Summer School on “Graph Theory and  Graph Algorithms” held at PSG College of Technology, Coimbatore, India, May 21- June 08, 2018.
• Invited talk on “Dominator Sequences in Hypercubes and the Forcing Set Conjecture” at the Symposium on “Interactions of Algebra and Discrete Mathematics”, 83^rd Annual Conference of Indian Mathematical Society, Sri Venkateshwara University, Tirupati, Andhra Pradesh, India, December 12-15, 2017.
• Invited talk on “AL-Matrix: Properties and Applications” at 5^th India-Taiwan Conference on Discrete Mathematics (ITCDM), Taipei, Taiwan, July 18 - 21, 2017.
• Series of lectures on “Interconnection Networks: Properties and Applications”, at Workshop on Interconnection Networks, Amrita University, Coimbatore, India, April 24-28, 2017
• Invited talk on “Network Sciences and Applications”, at Workshop on Interconnection Networks, Amrita University, Coimbatore, India, April 24-28, 2017.
• Invited talk on “A Novel Algorithm to reconstruct graph using pseudospectrum”, at International Conference on Discrete Mathematics (ICDM-2016), Siddaganga Institute of Technology, Tumkur, Karnataka, India, June 10, 2016.
• Invited Talk on LATEX: How and Why!, at SSN College of Engineering, Chennai, India April 19, 2013.
• Invited Talk on LATEX: What next!, at SSN College of Engineering, Chennai, India April 20, 2013.
• A series of lectures on “Cayley Graphs”, during the Summer student program, IMSc, India, June 4-7, 2012.
• Talk on “Information inequalities and complexity measures for graphs”, at Institute Seminar Week, IMSc, India, March 28, 2012.
• Invited Talk on “Structural Complexity of Networks”, at VIT University, Chennai, India February 16, 2012.
• Talk on “Information Inequalities for Networks”, at UMIT, Hall in Tirol, Austria, February 16, 2011.
• Talk on “Information Inequalities for Chemical Graphs”, at International Conference on Applied Mathematics, ICAM 7, Babes-Bolyai University, Cluj, Romania, September 02, 2010.
• Invited Talk on “Cycles and Chromatic Number”, at Kalasalingam University, Srivilliputhur, India, March 15, 2010.
• Invited speaker at the National Seminar on GTAAN’s at SCSVMV Deemed University, Kancheepuram, India, July 21, 2009.
• Invited Talk on “Embedding Trees in Hypercubes”, at SCSVMV Deemed University, Kancheepuram, India, July 15, 2009.
• Invited Talk on “Recent Trends in Graph Embeddings”, at School of Computer Science, University of Oklahoma, USA, April 03, 2009.

Seminars/ Conferences (Upcoming):

​GIAN Course on "Network Science and Multi-Agent Systems", To be announced later. 

Seminars/ Conferences/Events (Concluded):

• VI-India-Taiwan Conference on Discrete Mathematics (6th ITCDM-2019) during November 15 - 18 2019. 
  More details are available on the Conference Webpage (Click here) 

• ​​QIP& CEP Short Term Course on Advances in Graph Theory with Applications to Network Sciences during 6-11 August 2018. 
  http://www.agtans2018.iitbhu.ac.in 

For Prospective Ph.D. Positions

Prospective Ph.D. Students of my Group must have sound knowledge in mathematics  (especially in Graph Theory, Linear Algebra, Algebra) and Theoretical Computer Science (in Data structures and Algorithms).
Students interested to work on Network Science is desired to have knowledge of Machine learning, Probability and Statistics.
Students of Electrical engineering interested to work in graph theoretic applications of electrical networks are also welcome.  
 
Ph.D. interviews at IIT (BHU), in general, are held two times a year;  in May/June for odd semester and in November/December for even semester. The admission procedure details can be found on IIT (BHU) website. 

Postdoctoral Positions

Several postdoctoral funding options are available through external agencies, for example SERB-NPDF, NBHM, etc. If you are interested to apply for any of these fellowships with me as supervisor, please do not hesitate to contact me via email.