Hosoya Polynomial, Wiener Index, Coloring and Planar of Annihilator Graph of Zn

Abstract

Let R be a commutative ring with identity. We consider ΓB(R) an annihilator graph of the commutative ring R. In this paper, we find Hosoya polynomial, Wiener index, Coloring, and Planar annihilator graph of Zn denote ΓB(Zn) , with n= pm or n=pmq, where p, q are distinct prime numbers and m is an integer with m ≥ 1 .

Keywords

• annihilator graph of ring
• zero-divisor graph
• hosoya polynomial
• wiener index
• coloring graph and planar graph