We have computed here the 𝛾𝑡 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 𝛾𝑡(𝐺) ≥ 𝑒𝑐𝑐(𝐶(𝐺)) + 1 which appeared in [1].

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Manuscript Title:

ON SIX PLATONIC GRAPHS

Author:

T. KALAISELVI, YEGNANARAYANAN VENKATARAMAN

DOI Number:

DOI:10.17605/OSF.IO/5NX69

Published : 2022-01-10

About the author(s)

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

Full Text : PDF

Abstract

We have computed here the 𝛾𝑡 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 𝛾𝑡(𝐺) ≥ 𝑒𝑐𝑐(𝐶(𝐺)) + 1 which appeared in [1].


Keywords

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