A Note on the Double Total Graph \(T_u(Γ(R))\) and \(T_u(Γ(Z_n × Z_m))\) - Singh, Ngangom Rojitkumar; Dutta, Sanghita (Communications in Mathematics and Applications, 2021)
Considering a commutative ring \(R\) with unity as the set of vertices and two vertices \(x\) and \(y\) are adjacent if and only if \(u+(x+y) Z(R)\) for some \(u U(R)\), the resulting graph \(T_u(Γ(R))\) is known as the double total graph. In this paper we find the degree of any vertex in \(T_u(Γ(R))\) for a weakly unit fusible ring \(R\) and domination number of \(T_u(Γ(R))\) for any ring \(R\). Also, we investigate the properties of \(T_u(Γ(Z_n×Z_m))\) and characterize R in terms of toroidal \(T_u(Γ(R))\).