Abstract
Let G be a subgraph of the complete bipartite graph \(K_{l,m},{l \leq m}\), with \(e=qm+p>0\), \(0 \leq p <m\), edges. The maximal value of the sum of the squares of the degrees of the vertices of G is \(qm^2+p^2+ p (q+1)^2+(m-p) q^2\). We classify all graphs that attain this bound using the diagonal sequence of a partition.
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Neubauer, M.G. The sum of squares of degrees of bipartite graphs. Acta Math. Hungar. 171, 1–11 (2023). https://doi.org/10.1007/s10474-023-01379-7
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DOI: https://doi.org/10.1007/s10474-023-01379-7