Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3
On Energy of Prime Ideal Graph of a Commutative Ring Associated with Transmission-Based Matrices
Romdhini, M. U., Nawawi, A., Husain, S. K. S., Al-Sharqi, F., and Purnamasari, N. A.
Corresponding Email: [email protected]
Received date: 13 February 2024
Accepted date: 19 June 2024
Abstract:
This research explores the energy of the prime ideal graph of a commutative ring. The study demonstrates the energy formula of the graph associated with transmission-based matrices. Through research, the findings highlight the distance, Wiener-Hosoya, and distance signless Laplacian matrices. It should be noted that the distance and Wiener-Hosoya energies are always twice their spectral radius, meanwhile, it does not hold for distance signless Laplacian energy.
Keywords: prime ideal graph; energy of a graph; commutative ring; distance matrix; distance signless Laplacian matrix; Wiener-Hosoya matrix
