This study reveals that nonsplit graphs can possess up to four split maximal edge induced subgraphs, highlighting their structural characteristics.
A split graph is a graph in which the vertices can be partitioned into an independent set and a clique. We show that every nonsplit graph has at most four split maximal proper edge induced subgraphs. The exhaustive list of fifteen classes of nonsplit graphs having a split maximal proper edge induced subgraph is determined in this paper.
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Manikandan et al. (2025) studied this question.
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