id: 05904582
dt: j
an: 05904582
au: Harant, Jochen; Jendrol, Stanislav; Madaras, Tomáš
ti: Upper bounds on the sum of powers of the degrees of a simple planar graph.
so: J. Graph Theory 67, No. 2, 112-123 (2011).
py: 2011
pu: John Wiley \& Sons, New York, NY
la: EN
cc: 
ut: degree sum; planar graph
ci: 
li: doi:10.1002/jgt.20519
ab: Summary: For a simple planar graph $G$ and a positive integer $k$, we prove
    the upper bound $$2(n - 1)^{k} + 4^{k}(n - 4) + 2 \cdot 3^{k} -
    2\left((δ+ 1)^{k} - δ^{k}\right)(3n - 6 - m)$$ on the sum of the
    $k$th powers of the degrees of $G$, where $n, m$, and $δ$ 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 $δ= 3$. We also present upper bounds in terms of order, minimum
    degree, and maximum degree of $G$.
rv: