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In this paper, we consider the intersection graph $I_{\Gamma }\left(\mathbb{Z}ₙ\right)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which $I_{\Gamma }\left(\mathbb{Z}ₙ\right)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that $I_{\Gamma }\left(\mathbb{Z}ₙ\right)$ is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of $I_{\Gamma }\left(\mathbb{Z}ₙ\right)$.