 
Summary: Sum of squares of degrees in a graph
Bernardo M. ŽAbrego 1
Silvia FernŽandezMerchant1
Michael G. Neubauer
William Watkins
Department of Mathematics
California State University, Northridge
18111 Nordhoff St, Northridge, CA, 913308313, USA
email:{bernardo.abrego, silvia.fernandez,
michael.neubauer, bill.watkins}@csun.edu
February 12, 2008, final version
Abstract
Let G(v, e) be the set of all simple graphs with v vertices and e edges and let P2(G) = d2
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 quasistar graph or the quasicomplete 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) are the same for the quasistar and the quasicomplete
graph. In addition to the quasistar and quasicomplete graphs, we find all other graphs in
