The Double Total Graph of a Commutative Ring

A Note on the Double Total Graph T_u(Γ(R)) and T_u(Γ(Z_n×Z_m))

“…Let R be a finite commutative ring with unity. By [7,Theorem 2.11(2)], [2,Theorem 5.14] and [6,Proposition 4.1], it is enough to consider the following rings as G(R) is a spanning subgraph of T u (Γ(R)).…”

“…In general the total graph and the unit graph are disconnected. The double total graph [6] is a connected graph containing the unit graph of the ring as a subgraph ([6,Proposition 3.12]).…”

“…In Section 2 of this note, we find the degree of any vertex in T u (Γ(R)) for a weakly unit fusible ([6,Definition 3.7]) ring R and the domination number γ(T u (Γ(R))). In Section 3, we find properties of T u (Γ(Z n × Z m )).…”