Spectral Analysis of the Adjacency Matrix and Hamiltonian Properties of Zero-divisor Graphs
Keywords:
Complete bipartite Zero-divisor graph, Adjacency matrix, Spectral radius ????(????), Energy, Hamiltonian graphAbstract
This paper investigates the spectral properties of complete bipartite zero-divisor graphs Γ(ℤ????×ℤ????) and Γ(ℤ????[i]×ℤ????[????]). Our analysis's main focus is on the adjacency matrices of these graphs, proving several results on trace, singularity, and energy. Also, we demonstrate that these graphs are complete bipartite Hamiltonian graphs, containing Hamiltonian cycles of orders 2(????−1) and 2(????2−1) respectively.











