I am interested in Combinatorial Matrix Theory. In linear Combinatorial Matrix Theory, researchers study graph structures via different properties of matrices associated with it. Among the various matrices associated with a graph, the adjacency matrix is probably the most popular and widely investigated one. Sometimes different structural properties of a graph gets characterized by different properties of the eigenvalues and the eigenvectors of the associated adjacency matrix. For example, it is well know that ‘a (simple) connected graph G is bipartite if and only if −a is an eigenvalue of G whenever a is an eigenvalue of G’. There are many interesting results exhibiting the relationship of the graph structure with the eigenvalues and eigenvectors.
I am working to establish such relationships with regard to the concepts of inverse graph and reciprocal eigenvalue properties. In many ways these two concepts are related to each other. Both of these play important roles in quantum chemistry.
On the inverse of a class of bipartite graphs with unique perfect matchings by Panda S. K., Pati S. Electronic Journal of Linear Algebra 29 89-101 (2015)
Almost Self-inverse graphs by Bapat R. B., Panda S. K. Linear and Multilinear Algebra 67 2065-2076 (2019)
Strong reciprocal eigenvalue property of a class of weighted graphs by Bapat R. B., Panda S. K., Pati S. Linear Algebra and its Applications 511 460-475 (2016)
On some graphs which possess inverses by Panda S. K., Pati S. Linear and Multilinear Algebra 64 1445-1459 (2016)
Graphs with reciprocal eigenvalue properties by Panda S. K., Pati S. Electronic Journal of Linear Algebra 31 511-514 (2016)
Unicyclic graphs with bicyclic inverses by Panda S. K. Czechoslovak Mathematical Journal 67 1133-1143 (2017)
Self-inverse unicyclic graphs and strong reciprocal eigenvalue property by Bapat R. B., Panda S. K., Pati S. Linear Algebra and its Applications 531 459-478 (2017)
On some graphs which satisfy reciprocal eigenvalue properties by Panda S. K., Pati S. Linear Algebra and its Application 530 445-460 (2017)
Inverses of weighted graphs by Panda S. K., Pati S. Linear Algebra and its Applications 532 222-230 (2017)
Inverses of bicyclic graphs by Panda S. K. Electronic Journal of Linear Algebra 32 217-231 (2017)
Some results on the signless Laplacian permanental polynomial and star degree of balanced trees by Khan A., Panigrahi P., Panda S.K. Bulletin of the Institute of Combinatorics and its Applications 106 95-112 (2026)
Bounds on hypergraph energy and its variation under arbitrary hyperedge deletion by Saha S.S., Panda S.K. Linear Algebra and Its Applications 735 31-56 (2026)
Combinatorial description of the inverse of the adjacency matrix of non-bipartite bicyclic graphs by Sharma K., Panda S.K. Linear and Multilinear Algebra - (2026)
The P-vertex problem for symmetric matrices whose associated graphs admit perfect matchings by Sharma K., Panda S.K. Linear Algebra and Its Applications 731 109-138 (2026)
Recursive formulae for the Laplacian permanental polynomials of signed graphs by Khan A., Panigrahi P., Panda S.K. Discrete Mathematics, Algorithms and Applications - (2025)
On the Kirchhoff index of hypergraphs by Saha S.S., Panda S.K. Czechoslovak Mathematical Journal - (2025)
On the signless Laplacian spectrum of k-uniform hypergraphs by Bapat R.B., Saha S.S., Panda S.K. Linear and Multilinear Algebra - (2025)
Some results on the signless Laplacian permanental polynomial and star degree of balanced trees by Khan A., Panigrahi P. , Panda S. K. Bulletin of the Institute of Combinatorics and its Applications - (2025)
Some unicyclic graphs determined by the signless Laplacian permanental polynomial by Khan A., Panigrahi P. , Panda S. K. Journal of Applied Mathematics and Computing 70 2857-2878 (2024)
On the distance energy of k-uniform hypergraphs by Panda S. K., Sharma K. Special Matrices - (2023)
A study on determination of some graphs by Laplacian and signless Laplacian permanental polynomials by Khan A., Panigrahi P. , Panda S. K. AKCE International Journal of Graphs and Combinatorics 20 79-80 (2023)
On the Laplacian spectrum of k-uniform hypergraphs by Saha S.S., Sharma K., Panda S.K. Linear Algebra and Its Applications 655 1-27 (2022)
Strongly self-inverse weighted graphs by Berman A., Shaked-Monderer N., Panda S.K. Electronic Journal of Linear Algebra 36 80-89 (2020)
Almost Self-inverse graphs by Bapat R. B., Panda S. K. Linear and Multilinear Algebra 67 2065-2076 (2019)
The spectral radius of the reciprocal distance Laplacian matrix of a graph by Bapat R. B., Panda S. K. Bulletin of the Iranian Mathematical Society 44 1211-1216 (2018)
On some graphs which satisfy reciprocal eigenvalue properties by Panda S. K., Pati S. Linear Algebra and its Application 530 445-460 (2017)
On the inverse of a class of weighted graphs by Panda S. K., Pati S. Electronic Journal of Linear Algebra 32 539-545 (2017)
Self-inverse unicyclic graphs and strong reciprocal eigenvalue property by Bapat R. B., Panda S. K., Pati S. Linear Algebra and its Applications 531 459-478 (2017)
Unicyclic graphs with bicyclic inverses by Panda S. K. Czechoslovak Mathematical Journal 67 1133-1143 (2017)
Inverses of bicyclic graphs by Panda S. K. Electronic Journal of Linear Algebra 32 217-231 (2017)
Inverses of weighted graphs by Panda S. K., Pati S. Linear Algebra and its Applications 532 222-230 (2017)
Strong reciprocal eigenvalue property of a class of weighted graphs by Bapat R. B., Panda S. K., Pati S. Linear Algebra and its Applications 511 460-475 (2016)
Graphs with reciprocal eigenvalue properties by Panda S. K., Pati S. Electronic Journal of Linear Algebra 31 511-514 (2016)
On some graphs which possess inverses by Panda S. K., Pati S. Linear and Multilinear Algebra 64 1445-1459 (2016)
On the inverse of a class of bipartite graphs with unique perfect matchings by Panda S. K., Pati S. Electronic Journal of Linear Algebra 29 89-101 (2015)
Completed Projects
Principal Investigator
Self-inverse and Almost Self-inverse Graphs
On the Laplacian spectrum of hypergraphs
Alumni members
Ph. D. Students
Aqib (2025)
Area of Research: Spectral Graph Theory
Thesis Title: On the Determination of Some Graphs by Laplacian and Signless Laplacian Permanental Polynomials
Shib Sankar Saha (2025)
Area of Research: Combinatorial Matrix Theory
Thesis Title: On the spectrum of uniform hypergraphs
