The Total Graphs of Finite Rings

Abstract

In this paper we extend the study of total graphs τ(R) to noncommutative finite rings R. We prove that τ(R) is connected if and only if R is not local, and we see that in that case τ(R) is always Hamiltonian. We also find an upper bound for the domination number of τ(R) for all finite rings R.

Key Words:

• Finite ring
• Total graph
• Zero-divisor

2010 Mathematics Subject Classification:

• 16U99
• 05C25

Notes

Communicated by E. Puczylowski.