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On size, radius and minimum degree

Abstract : Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in terms of order, radius and minimum degree. Our result is a strengthening of an old classical theorem of Vizing (1967) if minimum degree is prescribed.
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Simon Mukwembi. On size, radius and minimum degree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 1 (1), pp.1--5. ⟨10.46298/dmtcs.1265⟩. ⟨hal-01179221⟩