Affiliation:
1. Department of Mathematics, Irbid National University, Irbid 21110, Jordan
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.
Funder
Irbid National University, Irbid, Jordan
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference21 articles.
1. Coloring of commutative rings;Beck;J. Algebra,1988
2. The zero-divisor graph of a commutative ring;Anderson;J. Algebra,1999
3. The total graph of a commutative ring;Anderson;J. Algebra,2008
4. Grimaldi, R.P. (1989, January 20–24). Graphs from rings. Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL, USA.
5. Unit graphs associated with rings;Ashrafi;Commun. Algebra,2010