CONSTRUCTING GRAPHS WITH FULL RANK ADJACENCY MATRICES

This work establishes a complete characterization of graph sizes that permit zero nullity configurations, where nullity denotes the multiplicity of zero in the adjacency spectrum. We prove three necessary conditions where graphs must exhibit non-zero nullity based on their edge count, and provide constructive methods to generate zero-nullity graphs for all other feasible sizes. The results resolve a problem in spectral graph theory with implications for molecular stability analysis in chemical graph theory.

کلیدواژه ها:

adjacency matrix ، zero nullity ، graph spectrum