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D. Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple graph is at most the number of vertices of the graph. This can be proved, in particular, for all regular graphs. Gernert's conjecture was recently disproved by one of the authors [4], who also provided a nontrivial upper bound for the sum of two largest(More)
—In this paper, a new topology for cascaded multilevel converter based on submultilevel converter units and full-bridge converters is proposed. The proposed topology significantly reduces the number of dc voltage sources, switches, IGBTs, and power diodes as the number of output voltage levels increases. Also, an algorithm to determine dc voltage sources(More)
—A new evolutionary algorithm known as the shuffled frog leaping algorithm is presented in this paper, to solve the unit commitment (UC) problem. This integer-coded algorithm has been developed to minimize the total energy dispatch cost over the scheduling horizon while all of the constraints should be satisfied. In addition, minimum up/down-time(More)
We present a polynomial time algorithm for multicasting rate h to N receivers over deterministic networks. Our algorithm requires intermediate network nodes to perform coding operations over vectors of a finite length L, through multiplication with L × L binary coding matrices that play the same role as coding coefficients over graphs. Our code(More)
The unit distance graph R is the graph with vertex set R 2 in which two vertices (points in the plane) are adjacent if and only if they are at Euclidean distance 1. We prove that the circular chromatic number of R is at least 4, thus improving the known lower bound of 32/9 obtained from the fractional chromatic number of R. 1. Introduction. The unit(More)
The unit distance graph R is the graph with vertex set R 2 in which two vertices (points in the plane) are adjacent if and only if they are at Euclidean distance 1. We prove that the circular chromatic number of R is at least 4, thus " tightening " the known lower bound on the chromatic number of R. 1. Introduction. The unit distance graph R is defined to(More)
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