In Das et al. (2013) [8], a new graph on monogenic semigroups (with zero) having elements has been recently defined. The vertices are the non-zero elements and, for , any two distinct vertices and are adjacent if in . As a continuing study, in Akgunes et al. (2014) [3], it has been investigated some well known indices (first Zagreb
index, second Zagreb
index,
Randi膰 index, geometric-arithmetic
index, atom-bond connectivity
index, Wiener
index, Harary
index, first and second Zagreb eccentricity indices, eccentric connectivity
index, the degree distance) over .
In the light of above references, our main aim in this paper is to extend these studies over to the tensor product. In detail, we will investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the tensor product of any two (not necessarily different) graphs and .