2023/03/15 by P. Jamsheena, Jamsheena, P., A V Chithra +2
Mathematics · Computer Science · #Graph theory and applications #Interconnection Networks and Systems #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2303.08468
Let R be a commutative ring with unity. The essential ideal graph ER of R, is a graph with a vertex set consisting of all nonzero proper ideals of R and two vertices I and K are adjacent if and only if I+ K is an essential ideal. In this paper, we study the adjacency spectrum of the essential ideal graph of the finite commutative ring ℤn, for n=\pm, p^m1q^m2\, where p,q are distinct primes, and m,m1, m2∈ \mathbb N. We show that 0 is an eigenvalue of the adjacency matrix of E_ℤn if and only if either n= p2 or n is not a product of distinct primes. We also determine all the eigenvalues of the adjacency matrix of E_ℤn whenever n is a product of three or four distinct primes. Moreover, we calculate the topological indices, namely the Wiener index and hyper-Wiener index of the essential ideal graph of ℤn for different forms of n