Abstract
The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.
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