A ug 2 00 8 Sum of squares of degrees in a graph

@inproceedings{brego2008AU2,
  title={A ug 2 00 8 Sum of squares of degrees in a graph},
  author={Bernardo M. {\'A}brego and Silvia Fern{\'a}ndez-Merchant and Michael G. Neubauer and William Watkins},
  year={2008}
}
Let G(v, e) be the set of all simple graphs with v vertices and e edges and let P2(G) = ∑ d i denote the sum of the squares of the degrees, d1, . . . , dv, of the vertices of G. It is known that the maximum value of P2(G) for G ∈ G(v, e) occurs at one or both of two special graphs in G(v, e)—the quasi-star graph or the quasi-complete graph. For each pair (v, e), we determine which of these two graphs has the larger value of P2(G). We also determine all pairs (v, e) for which the values of P2(G… CONTINUE READING