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2014
Journal Article
Titel
On degree sums of a triangle-free graph
Abstract
For a simple triangle-free k-chromatic graph G with k >= 2 the upper bound m(n-f (k-2)) on the sum Sigma(2)(G) = Sigma(x is an element of V(G))d(2)(x) of the squares of the degrees of G is proved, where n, m, and f(1) are the order of G, the size of G, and the minimum order of a triangle-free l-chromatic graph, respectively. Consequences of this bound are discussed. Moreover, we generalize the upper bound on Ep (G) = Sigma(p)(G) = Sigma(x is an element of V(G))d(x)) for p = 2 to P >= 3.