منابع مشابه
Parity-regular Steinhaus graphs
Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n−1. A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic binary sequences 110...110 of any length n − 1 = 3m. By an exhaustive search the conjecture was known to hold up to 25 vertices. We report h...
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A Steinhaus matrix is a binary square matrix of size n which is symmetric, with diagonal of zeros, and whose upper-triangular coefficients satisfy ai,j = ai−1,j−1+ai−1,j for all 2 6 i < j 6 n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states...
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In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.
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A generalized Steinhaus graph of order n and type s is a graph with n vertices whose adjacency matrix (a i;j) satisses the relation a i;j =
متن کاملUniform generalized Steinhaus graphs
In [1] it is shown that the first order theory of almost all generalized Steinhaus graphs is identical to the first order theory of almost all where each generalized Steinhaus graph is given the same probability. A natural probability measure on generalized Steinhaus graphs is obtained by independently assigning a probability of p for each entry in the generating string of the graph. With this ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-07-02063-7