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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)
Li, X. and F. Zhang, On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs, Discrete Mathematics 94 (1991) 189-197. In this paper, we give the spectra and characteristic polynomials of generalized de Bruijn graphs. By Tutte’s Theorem we can obtain the number of spanning trees and the number of Eulerian tours in such graphs.
BACKGROUND This study retrospectively reviewed 48 cases of gastric submucosal tumors (SMTs) treated by endolumenal endoscopic full-thickness resection (EFR) microsurgery in our gastrointestinal endoscopy center. PATIENTS AND METHODS From November 2009 to October 2012, 48 cases underwent endolumenal EFR for resection of muscularis propria-originating(More)
Given a graph G = (V, E) and a (not necessarily proper) edge-coloring 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 cardi-nality in two(More)
A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d w (v) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted(More)
Let G = (V, E) be an (edge-)colored graph, i.e., G is assigned a mapping C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is(More)