We consider the higher-order nonlinear difference equation x n1 p qx n−k /1 x n rx n−k , n 0, 1,. .. with the parameters, and the initial conditions x −k ,. .. , x 0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open problem introduced by Kulenovi´cKulenovi´c and Ladas in their monograph see Kulenovi´cKulenovi´c and Ladas, 2002.

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Let G be a simple graph of order n and μ 1 , μ 2 , . . . , μ n the roots of its matching polynomial. The matching energy of G is defined as the sumIn this paper, we show that K k n-1,1 has the maximum matching energy among the connected graphs with order n and edge connectivity k.

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