Some Bench Mark Results on Total Domination Subdivision Stable Graph

For a graph G, the total dominating set defined as a set of vertices in S such that all the vertices in V(G) has at least one neighbor in S, the least cardinality is noted as t(G). The total domination number of each and every graph while subdividing any edge xy of G is equal to the total domination number of G, which results in the total domination subdivision stable graph abbreviated as TDSS and the symbolic expression is Gtsd(xy). The research paper, we introduce TDSS and proposed conditions under which a graph is TDSS and not TDSS.