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In this note we give an explanation for two phenomena mentioned in the concluding remarks of “The matching polynomial of a polygraph” by Babic et al. The following results are obtained: (1) Although three matrices for given polygraphs defined in the above article in general have different orders, they determine the same recurrence relations for the matching(More)
Let G be an (edge-)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those for the existences of long heterochromatic paths and cycles(More)
BACKGROUND The prevalence of Helicobacter pylori is higher in developing countries. The aim of this study was to investigate the prevalence and risk factors of H. pylori infection in areas with high prevalence of gastric cancer in Jiangsu Province, China. METHODS A prospective epidemiologic survey of H. pylori infection was accomplished in a natural(More)
In the original paper, Goldman et al. (2000) launched the study of the inverse problems in combinatorial chemistry, which is closely related to the design of combinatorial libraries for drug discovery. Following their ideas, we investigate four other topological indices, i.e., the sigma-index, the c-index, the Z-index, and the M(1)-index, with a special(More)
The general Randić index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randić index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randić in 1975. The paper outlines the(More)
Given a graph G = (V,E) and a (not necessarily proper) edgecoloring of G, we consider the complexity of finding a spanning tree of G with as many different colors as possible, and of finding one with as few different colors as possible. We show that the first problem is equivalent to finding a common independent set of maximum cardinality in two matroids,(More)
Power efficiency is increasingly critical to battery-powered smartphones. Given the using experience is most valued by the user, we propose that the power optimization should directly respect the user experience. We conduct a statistical sample survey and study the correlation among the user experience, the system runtime activities, and the minimal(More)