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Neubauer, Silvia Fern\\'andez-Merchant, William Watkins","submitted_at":"2008-08-16T03:27:11Z","abstract_excerpt":"Let $\\G(v,e)$ be the set of all simple graphs with $v$ vertices and $e$ edges and let $P_2(G)=\\sum d_i^2$ denote the sum of the squares of the degrees, $d_1, >..., d_v$, of the vertices of $G$.\n  It is known that the maximum value of $P_2(G)$ for $G \\in \\G(v,e)$ occurs at one or both of two special graphs in $\\G(v,e)$--the \\qs graph or the \\qc graph. For each pair $(v,e)$, we determine which of these two graphs has the larger value of $P_2(G)$. We also determine all pairs $(v,e)$ for which the values of $P_2(G)$ are the same for the \\qs and the \\qc graph. 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