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181.
Let H{\mathcal{H}} be a set of disjoint faces of a cubic bipartite polyhedral graph G. If G has a perfect matching M such that the boundary of each face of H{\mathcal{H}} is an M-alternating cycle (or in other words, G-H{G-\mathcal{H}} has a perfect matching), then H{\mathcal{H}} is called a resonant pattern of G. Furthermore, G is k-resonant if every
i (1 \leqslant i \leqslant k){i\,(1\,\leqslant\, i\, \leqslant\, k)} disjoint faces of G form a resonant pattern. In particular, G is called maximally resonant if G is k-resonant for all integers
k \geqslant 1{k\,\geqslant\, 1}. In this paper, all the cubic bipartite polyhedral graphs, which are maximally resonant, are characterized. As a corollary,
it is shown that if a cubic bipartite polyhedral graph is 3-resonant then it must be maximally resonant. However, 2-resonant
ones need not to be maximally resonant. 相似文献
182.
In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an “asymptotically good” upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined. 相似文献
183.
In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187?C1208, 2007) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The ??BB method, used widely in global optimization, is applied to construct the convexification relaxation. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve NSIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the NSIP problems. In addition, some NSIP application examples are implemented by the method proposed in this paper, such as the proportional-integral-derivative controller design problem and the nonlinear finite impulse response filter design problem. Based on our numerical experience, we demonstrate that our algorithm enhances the computational speed for solving NSIP problems. 相似文献