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Sum of squares of degrees in a graph Bernardo M. Abrego 1
 

Summary: Sum of squares of degrees in a graph
Bernardo M. ŽAbrego 1
Silvia FernŽandez-Merchant1
Michael G. Neubauer
William Watkins
Department of Mathematics
California State University, Northridge
18111 Nordhoff St, Northridge, CA, 91330-8313, 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 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) are the same for the quasi-star and the quasi-complete
graph. In addition to the quasi-star and quasi-complete graphs, we find all other graphs in

  

Source: Abrego, Bernardo - Department of Mathematics, California State University, Northridge
Fernandez, Silvia - Department of Mathematics, California State University, Northridge

 

Collections: Mathematics