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\iteman{io-port 05904582}
\itemau{Harant, Jochen; Jendrol, Stanislav; Madaras, Tom\'a\v{s}}
\itemti{Upper bounds on the sum of powers of the degrees of a simple planar graph.}
\itemso{J. Graph Theory 67, No. 2, 112-123 (2011).}
\itemab
Summary: For a simple planar graph $G$ and a positive integer $k$, we prove the upper bound $$2(n - 1)^{k} + 4^{k}(n - 4) + 2 \cdot 3^{k} - 2\left((\delta + 1)^{k} - \delta ^{k}\right)(3n - 6 - m)$$ on the sum of the $k$th powers of the degrees of $G$, where $n, m$, and $\delta $ are the order, the size, and the minimum degree of $G$, respectively. The bound is tight for all $m$ with $0 \leq 3n - 6 - m \leq \lfloor n/2\rfloor - 2$ and $\delta = 3$. We also present upper bounds in terms of order, minimum degree, and maximum degree of $G$.
\itemrv{~}
\itemcc{}
\itemut{degree sum; planar graph}
\itemli{doi:10.1002/jgt.20519}
\end