The sum of the squares of degrees: Sharp asymptotics
โ Scribed by Vladimir Nikiforov
- Book ID
- 108113787
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 133 KB
- Volume
- 307
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Among all simple graphs on n vertices and e edges, which ones have the largest sum of squares of the vertex degrees? It is easy to see that they must be threshold graphs, but not every threshold graph is optimal in this sense. Boesch et al. [Boesch et al., Tech Rep, Stevens Inst Tech, Hoboken NJ, 19
Let G be a simple graph with n vertices, e edges and vertex degrees &, d2 ..... d~. It is proved that d2+ ... +d~<~e(2e/(n-1)+ n-2) when n~>2. This bound does not generalize to all sequences of positive integers. A comparison is made to another upper bound on d 2 +. โข -+ d 2, due to Sz6kely et al. (
The absolutely convergent exponential sum is studied for m โ +โ and fixed p when the parameter ฮธ is allowed to become large such that ฮธ/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of S p (ฮธ; m) consisting of a multiple spiral struc