A note on distance-hereditary graphs whose complement is also distance-hereditary
arXiv:2504.1285719.1h-index: 2
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This is an incremental theoretical contribution for graph theory researchers.
The paper tackled the problem of characterizing distance-hereditary graphs whose complements are also distance-hereditary, and the result was a characterization using split decomposition and modular decomposition.
Distance-hereditary graphs are known to be the graphs that are totally decomposable for the split decomposition. We characterise distance-hereditary graphs whose complement is also distance-hereditary by their split decomposition and by their modular decomposition.