This analysis discusses domination integrity in different graph types, highlighting implications for graph vulnerability.
The domination integrity DI(G) of a simple connected graph G is defined as DI(G) = min{| X | +m(G−X) : X is a dominating set } where m(G−X) is the order of a maximum connected component of G − X. It is a measure of vulnerability of a graph. This work is aimed to discuss domination integrity of middle graph of crown graph, middle graph of tadpole graph, middle graph of friendship graph, christmas Star Graph and kusudama flower graph.
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Shah et al. (2025) studied this question.
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