1. T. KALAISELVI - Department of Mathematics, Kalasalingam Academy of Research and Education
Krishnankovil-626126.

2. YEGNANARAYANAN VENKATARAMAN - Department of Mathematics, Kalasalingam Academy of Research and Education
Krishnankovil-626126

We have computed here the 𝛾_{𝑡} refereed as total domination number of the six platonic graphs. Incidentally we found that the octahedron graph is a counter example to the following result: If G is a connected graph of order at least two, then 𝛾_{𝑡}(𝐺) ≥ 𝑒𝑐𝑐(𝐶(𝐺)) + 1 which appeared in [1].

Domination set (DS), total domination set (TDS), Domination number (DN), total domination number (TDN), Platonic Graphs.