The Geodetic Number for the Unit Graphs Associated with Rings of Order <i>P</i> and <i>P</i>²

Abstract

Let G(R) be the unit graph associated with a ring R. Let p be a prime number and let R be a finite ring of order p or p2 and be one of the rings Zp,Zp2,GF(p2),Zp(+)Zp or Zp×Zp. We determine the geodetic number g(G(R)) associated with each such ring.

Keywords

• commutative ring
• finite field
• unit graph
• geodetic set
• geodetic number