Eigenvalues and Wiener index of the Zero Divisor graph Γ[\mathbb Z_n]

2017/07/17 by Reddy, B. Surendranath, Jain, Rupali. S., Laxmikanth, N.
#05C12 #05C50 #13A99 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1707.05083

Abstract

The Zero divisor Graph of a commutative ring R, denoted by Γ[R], is a graph whose vertices are non-zero zero divisors of R and two vertices are adjacent if their product is zero. In this paper, we consider the zero divisor graph Γ[ℤ_n] for n=p³ and n=p²q with p and q primes. We discuss the adjacency matrix and eigenvalues of the zero divisor graph Γ[ℤ_n]. We also calculate the energy of the graph Γ[ℤ_n].

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