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Let G be a simple connected graph of order n with degree sequence d 1 , d 2 , · · · , d n in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer at most n, we give a sharp upper bound for ρ(G) by a function of d 1 , d 2 , · · · , d , which generalizes a series of previous results.
Silicon nanowire possesses great potential as the material for renewable energy harvesting and conversion. The significantly reduced spectral reflectivity of silicon nanowire to visible light makes it even more attractive in solar energy applications. However, the benefit of its use for solar thermal energy harvesting remains to be investigated and has so… (More)
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for… (More)