Abstract
In 2016, Lumduanhom et al. determined all graphs of size m with PC-number or SPC-number m−1, m−2, m−3. But we find that the graphs with SPC-number m−3 are not completely characterized. In this article, we characterize all graphs with SPC-number m−3. Moreover, we present all graphs satisfying PC-number or SPC-number m−4.
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