منابع مشابه
Efficient Enumeration of All Ladder Lotteries
A ladder lottery, known as “Amidakuji” in Japan, is a common way to choose one winner or to make an assignment randomly in Japan. Formally, a ladder lottery L of a permutation π = (x1, x2, . . . , xn) is a network with n vertical lines (lines for short) and many horizontal lines (bars for short) connecting two consecutive vertical lines. The top ends of lines correspond to π. See Fig. 1. Each n...
متن کاملThe birank number of ladder, prism and Mobius ladder graphs
Given a graph G, a function f : V (G)→ {1, 2, ..., k} is a k-biranking of G if f(u) = f(v) implies every u-v path contains vertices x and y such that f(x) > f(u) and f(y) < f(u). The birank number of a graph, denoted bi(G), is the minimum k such that G has a k-biranking. In this paper we determine the birank numbers for ladder, prism, and Möbius ladder graphs.
متن کاملEnumeration of cospectral graphs
We have enumerated all graphs on at most 11 vertices and determined their spectra with respect to various matrices, such as the adjacency matrix and the Laplacian matrix. We have also counted the numbers for which there is at least one other graph with the same spectrum (a cospectral mate). In addition we consider a construction for pairs of cospectral graphs due to Godsil and McKay, which we c...
متن کاملEnumeration of Difference Graphs
A difference graph is a bipartite graph G = (X, Y: E) such that all the neighborhoods of the vertices of X are comparable by inclusion. We enumerate labeled and unlabeled difference graphs with or without a bipartition of the vertices into two stable sets. The labeled enumerations are expressed in terms of combinatorial numbers related to the Stirling numbers of the second kind.
متن کاملEfficient Enumeration of All Ladder Lotteries with k Bars
A ladder lottery, known as the “Amidakuji” in Japan, is a common way to choose an assignment randomly. Formally, a ladder lottery of a permutation π = (p1, p2, . . . , pn) is a network with n vertical lines (lines for short) and many horizontal lines (bars for short) as follows (see Fig. 1). The i-th line from the left is called line i. The top ends of the n lines correspond to π. The bottom en...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1974
ISSN: 0012-365X
DOI: 10.1016/0012-365x(74)90081-8