Spectral Analysis of the Adjacency Matrix and Hamiltonian Properties of Zero-divisor Graphs

Authors

  • S. G. Jakkewad
  • R. G. Metkar
  • V Murgan
  • P. Tekalkar

Keywords:

Complete bipartite Zero-divisor graph, Adjacency matrix, Spectral radius ????(????), Energy, Hamiltonian graph

Abstract

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.

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Published

2025-04-21

How to Cite

S. G. Jakkewad, R. G. Metkar, V Murgan, & P. Tekalkar. (2025). Spectral Analysis of the Adjacency Matrix and Hamiltonian Properties of Zero-divisor Graphs. Utilitas Mathematica, 122(1), 195–206. Retrieved from http://utilitasmathematica.com/index.php/Index/article/view/2102

Issue

Vol. 122 No. 1 (2025): Volume 122, 2025

Section

Articles

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