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In this paper, we consider the spectral radius of signless p-Laplacian of a graph, which is a generalization of the quadratic form of the signless Laplacian matrix for p = 2. Let G n , β be the set of simple graphs of order n with a given matching number β. In this paper, the graphs maximizing the largest signless p-Laplacian eigenvalue among G n , β are obtained. [ABSTRACT FROM AUTHOR]

BACKGROUND Dimethyl sulfide ( DMS) is a gaseous odor pollutant with very low threshold values that has serious impacts on environment quality and human health. The study reports a microwave catalytic reactor with V2O5/γ- Al2O3 catalyst for oxidation decomposition of dimethyl sulfide. RESULTS A combination of microwave and V2O5/γ- Al2O3 or microwave combined with V2O5/γ- Al2O3 and ozone as an oxidant completely converted DMS. The effect of DMS removal using microwave and V2O5/γ- Al2O3 is close to that of catalytic oxidizing of DMS using ozone and V2O5/γ- Al2O3. Microwave accentuates catalytic oxidation of DMS, and increases DMS removal efficiency. The addition of ozone to microwave catalysis over V2O5/γ- Al2O3 leads to the enhancement of DMS removal. ( CH3) 2SO, HCOOCH3 and SCO species are formed in the microwave catalytic DMS reaction. The mechanism of microwave catalytic DMS over V2O5/γ- Al2O3 was dominated by a free radical oxidation route. ( CH3) 2SO, ( CH3) 2SO2, SCO and CH3OH species are formed in the microwave catalytic oxidation of DMS. CONCLUSION Ozone enhances free radical formation. Oxidative reactions involving ozone and radicals play the dominant role in the destruction of DMS molecules using a microwave combined with V2O5/γ- Al2O3 catalyst using ozone as an oxidant. © 2013 Society of Chemical Industry [ABSTRACT FROM AUTHOR]