3 papers
math.CO2026
Zero-sum Inverse Realization and Property~(P) under Join Operations
G. Arunkumar, Anubhab Pahari, Puja Samanta
We introduce zero-sum inverse realization of property (P) of a graph , obtained by imposing an additional condition \( \mathbf{1}^{\top}A^{-1}\mathbf{1}=0, \) on a matrix $A\in…
math.CO2026
The Cycle Rank Threshold: Perfect Matchings and Bipartite Parter Graphs
G. Arunkumar, Puja Samanta
A graph on \(n\) vertices is called a Parter graph if there exists a nonsingular symmetric matrix, whose nonzero off-diagonal entries correspond exactly to the edges of the graph,…
math.CO2025
The Full P-vertex Problem and Perfect Matchings for Bipartite Graphs
G. Arunkumar, Puja Samanta
In a recent work, Sharma and Panda~\cite{sharma} showed that every bipartite graph with a perfect matching has property (P), and proved the converse for trees and unicyclic biparti…