Education

Degree: Ph.D. Mathematics,  15 February 2021, University of Kashmir, 190001, Kashmir. 

Title of Thesis: On Distribution of Laplacian Eigenvalues of Graphs, see Arxiv , Shodhganga 

Profile Links: Google Scholar , Research Gate , Scopus , Orcid, Web of Science, MathSciNet, 

Postdoc Advisors: Mustapha Aouchiche, Muhammad Imran, Zahid Raza 

Ph.D. Advisors: Shariefuddin Pirzada and Tariq Ahmad Chishti 

Mentors/Collaborators: Hilal Ahmad Ganie, Kinkar Chandra Das, Yilun Shang, Fawad Ali

Prior Education: 

• Post Graduate Diploma in Computer Applications (2017), University of Kashmir, Kashmir, India. 

Dissertation:  Solution of various problems in numerical analysis using C programming.

• Bachelor of Education (Mathematics Teaching, Principles of Education, Psychology of Learning) (2015), University of Kashmir, Srinagar Kashmir, India.

• M.Sc. Mathematics (2013), University of Kashmir, Srinagar Kashmir, India.

Major Courses: Real Analysis I and II, Abstract Algebra I and II, Functional Analysis I and II, General Topology, Linear Algebra, Numerical Analysis, Mathematical Statistics I and II, Measure Theory, Programming, Graph Theory, Mathematical Modelling, Differential  and Partial differential equations, Number theory I and II, Complex Analysis I and II, Analytic Polynomial theory, Differential Geometry.

• B.Sc. (Electronics, Physics, Mathematics) (2011), University of Kashmir, Srinagar Kashmir, India. 

• JKSET (Jammu and Kashmir State Eligibility Test for Assistant Professorship) (2018).

Erdős Number : 3 (Bilal Ahmad Rather ➟ Vilmar Trevisan ➟ Wayne Dean Goddard ➟ Paul Erdős)

Work Experience:

1. Working as post doctoral fellow from April 2021 to present date, under the joint supervision of Dr. Mustapha Aouchiche, Dr. Muhammad Imran and Dr. Adama Diene at Mathematical Sciences Department, United  Arab Emirates University, Al Ain 15551, Abu Dhabi, UAE.

2. Worked as guest lecturer from February 2021 to March 2021 at JK Institute of Mathematical Sciences, Srinagar Kashmir, India.

3. Worked as junior research fellow from August 2017 to June  2019 on SERB-DST(EMR/ 2015/0010471) major research project entitled  ``On energy and Laplacian energy of graphs'' at Department of Mathematics, University of Kashmir, Srinagar Kashmir, India.

Awards/Nominations and Recognitions:

1. Post doctoral fellowship at Department of Mathematics, Indian Institute of Technology, Guwahati, India, 2023-2024.

2. Post doctoral fellowship at Department of Mathematics, Shandong University of Science and Technology, Zibo, China, 2022.

3. Post doctoral fellowship at Department of Mathematics, University of Sharjah, Sharjah, UAE 2023.

4. Post doctoral fellowship at Mathematical Sciences Department, United  Arab Emirates University, Al Ain 15551, Abu Dhabi, UAE, 2021.

5. Nominated for Annual Research Awards 2021 by Dr K. V. Rao Scientific Society (KVRSS) Hyderabad, for the paper entitled "Distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of  Z_n,  Linear and Multilinear Algebra 70(17) (2022) 3354-3369"

6. JKSET (state eligibility test for assistant professorship/lectureship), 2018.

7. Junior research fellowship for a period of two years on SERB-DST(EMR/ 2015/0010471) major research project with the principal investigator Prof S. Pirzada,  entitled  ``On energy and Laplacian energy of graphs'' at Department of Mathematics, University of Kashmir, Srinagar Kashmir, India.

Representative Publications

1. Bilal Ahmad Rather, A note on the distinct eigenvalues of quotient matrices, Indian Journal of Pure and Applied Mathematics (2023), https://doi.org/10.1007/s13226-023-00448-5

2. Bilal Ahmad Rather, Hilal A. Ganie and Y. Shang, Distance Laplacian eigenvalues of sun graphs, Applied Mathematics and Computations 445 (2023), Article id 127847, https://doi.org/10.1016/j.amc.2023.127847

3. Bilal Ahmad Rather, X. Gao and J. Wang, Spectral spread and energy of eccentricity matrix, Discrete Applied Mathematics 352 (2024) 9--19, https://doi.org/10.1016/j.dam.2024.03.020.

4. Hilal A. Ganie and Bilal Ahmad Rather, On distance Randic eigenvalues and energy of graphs, Bulletin of the Brazilian Mathematical Society, New Series 53 (2022) 1449--1467, https://doi.org/10.1007/s00574-022-00312-w

5. Bilal Ahmad Rather, V. Bioda and M. Aouchiche , On distance (Laplacian) characteristic polynomials of power graphs, Journal of Algebra and its Applications (2023), https://doi.org/10.1142/S0219498825500033. 

6. Bilal Ahmad Rather, M. Imran and A. Diene, The linear strand of edge ideals of comaximal graphs of commutative rings, Communications in Algebra 52(4) (2024)1486--1500, https://doi.org/10.1080/00927872.2023.2263559. 

7. S. Pirzada, Bilal Ahmad Rather and M. Aouchiche, On eigenvalues and energy of geometric-arithmetic matrix of graphs, Mediterranean Journal of Mathematics19(115) (2022) https://doi.org/10.1007/s00009-022-02035-0

8. M. Aouchiche, Bilal Ahmad Rather and I. El Hallaoui, On the Gresgorin discs of distance matrices of graphs, Electronic Journal of Linear Algebra 37 (2021) 709--717. http://doi.org/10.13001/ela.2021.6489

9. S. Pirzada, Bilal Ahmad Rather, M. Aijaz and T. A. Chishti, Distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of  Z_n,  Linear and Multilinear Algebra 70(17) (2022) 3354-3369, http://doi.org/10.1080/03081087.2020.1838425

10. Hilal A. Ganie, S. Pirzada, Bilal Ahmad Rather and V. Trevisan, Further developments on Brouwer's conjecture for the sum of Laplacian eigenvalues of graphs, Linear Algebra  and its Applications 588 (2020) 1-18. https://doi.org/10.1016/j.laa.2019.11.020

Research Interests:

• Eigenvalue and eigenvector properties of adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and generalized adjacency matrix.

• Spectral properties of distance, distance Laplacian, distance signless Laplacian and generalized distance matrix.

• Spectral analysis of power graphs and commuting graphs of finite groups and zero-divisor graphs of finite commutative rings.

• Spectral properties of Geometric-Arithmetic matrix (index), Sombor matrix (index) of graphs, spectral invariants like energy, energy like invariant and graph parameters related to graph matrices.

• Betti numbers, projective dimension, regularity of the linear strand of edge ideals.

• Independent, domination and independent domination polynomials of graphs and their zeros

Professional Memberships:

• International Linear Algebra Society (ILAS)

• Kashmir Mathematical Society (KMS)