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arXiv · 2107.10660

Characterizations for split graphs and unbalanced split graphs

Hany Ibrahim
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Abstract

We introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ($2K_{2}$, claw)-free graph with $α(G) \geq 3$ is a split graph. Also, we apply it to characterize any pseudo-split graph. Finally, by using edge contraction again, we characterize unbalanced split graphs which we use to characterize the Nordhaus-Gaddum graphs.

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Hany Ibrahim. 2022-05-04. Characterizations for split graphs and unbalanced split graphs. https://arxiv.org/abs/2107.10660

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