11 research outputs found
Representing integers as linear combinations of powers
At a conference in Debrecen in October 2010 Nathanson announced some results
concerning the arithmetic diameters of certain sets. He proposed some related
results on the representation of integers by sums or differences of powers of 2
and 3. In this note we prove some results on this problem and the more general
problem about the representation by linear combinations of powers of some fixed
integers.Comment: 8 pages, paper will appear in Publ. Math. Debrece
Sharp Bounds for the Signless Laplacian Spectral Radius in Terms of Clique Number
In this paper, we present a sharp upper and lower bounds for the signless
Laplacian spectral radius of graphs in terms of clique number. Moreover, the
extremal graphs which attain the upper and lower bounds are characterized. In
addition, these results disprove the two conjectures on the signless Laplacian
spectral radius in [P. Hansen and C. Lucas, Bounds and conjectures for the
signless Laplacian index of graphs, Linear Algebra Appl., 432(2010) 3319-3336].Comment: 15 pages 1 figure; linear algebra and its applications 201