6 papers
Exponential Lower Bounds for the Pfaffian Number of Graphs
Priyanshu Pant, Ranveer Singh
The Fisher--Kasteleyn--Temperley (FKT) algorithm counts perfect matchings in planar graphs in polynomial time using a single Pfaffian computation. Galluccio--Loebl and Tesler exten…
On Chollet's Permanent Conjecture for Graph Laplacians
Priyanshu Pant, Ranveer Singh
In 1982, Chollet conjectured that for Hermitian positive semidefinite matrices , where denotes the Hadamard…
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…
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…