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Let G be an undirected connected graph with n vertices and m edges, n ≥ 3, and let μ1 ≥ μ2 ≥ . . . ≥ μn-1 > μn = 0 and ρ1 ≥ ρ2 ≥ . . . ≥ ρn-1 > ρn = 0 be Laplacian and normalized Laplacian Peigenvalues of G, respectively. The Laplacian-energy-like (LEL) invariant of graph G is defined as LEL(G) = Σn-1i=1 √μi. The Laplacian incidence energy of graph is defined as LIE(G) =Σn-1i=1 √ρi. In this paper, we consider lower bounds of graph invariants LEL(G) and LIE(G) in terms of some graph parameters, that refine some known results. [ABSTRACT FROM AUTHOR]

In this paper, we extend the arithmetic (AR) expressions for functions on finite dyadic groups to functions used in Fibonacci interconnection topologies. We have introduced the Fibonacci-Arithmetic (FibAR) expressions for representation of these functions. We discussed the optimization of FibARs with respect to the number of non-zero coefficients through the Fixed-Polarity FibARs defined by using different polarities for the Fibonacci variables. In this way, we provide a base to extend the application of ARs and related powerful CAD design tools for switching functions to functions in Fibonacci interconnection topologies. [ABSTRACT FROM AUTHOR]