7 papers
An Odd Pfaffian Number
Priyanshu Pant, Ranveer Singh
The Pfaffian number of a graph is the minimum number of Pfaffians needed to obtain its perfect-matching polynomial by linear combination. In 2009, Norine conjectured that every Pfa…
Exponential Lower Bounds for the Pfaffian Number of Graphs
Priyanshu Pant, Ranveer Singh
Galluccio--Loebl and Tesler showed that the perfect-matching polynomial of a graph embedded in an orientable surface of genus can be written as a linear combination of at most…
Structural Classes for Chollet's Permanent Conjecture
Priyanshu Pant, Ranveer Singh
In 1982, Chollet conjectured that for Hermitian positive semidefinite matrices , where de…
Permanental Energy of Graphs
Priyanshu Pant, Ranveer Singh
For a simple graph with adjacency matrix , let be its permanental polynomial with roots , and define the pe…
Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices
Priyanshu Pant, Surabhi Chakrabartty, Ranveer Singh
The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of th…
Permanent of bipartite graphs in terms of determinants
Surabhi Chakrabartty, Ranveer Singh
Computing the permanent of a -matrix is a well-known -complete problem. In this paper, we present an expression for the permanent of a bipartite graph in terms of the d…
Computing the permanental polynomial of -intercyclic bipartite graphs
Ravindra B. Bapat, Ranveer Singh, Hitesh Wankhede
Let be a bipartite graph with adjacency matrix . The characteristic polynomial and the permanental polynomial are bo…