Another class of balanced graph designs: balanced circuit designs
نویسندگان
چکیده
منابع مشابه
Balanced Nested Designs and Balanced n-ary Designs
We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...
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Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...
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Abstract A G-design is said to be balanced if the degree of its vertices is constant. We say that a G-design is strongly balanced, if for every i = 1, 2, ..., h, there exists a constant Ci such that dAi(x) = Ci, for every vertex x, where Ai indicates an automorphism classes (orbits) of the automorphism group of G, on its vertex-set, and dAi(x) is the number of blocks containing x as an element ...
متن کاملt-Wise Balanced Designs
Steiner 3-wise balanced designs are constructed for parameters 3-(3n − 1, {4, 8}, 1), 3(qnm− qm, {q− 1, q, q+ 1}, 1), 3-(qnm− 2qm− 1, {qm− 3, qm− 2, qm− 1, qm, qm+ 1}, 1), 3-(qnm − 2qm, {qm − 3, qm − 2, qm − 1, qm, qm + 1}, 1), 3-(qnm − 2qm + 1, {qm − 3, qm − 2, qm−1, qm, qm+1}, 1), where q is a prime power and n ≥ 2, m ≥ 1 are integers. Further designs are obtained from these. © 2008 Elsevier ...
متن کاملSome Pairwise Balanced Designs
A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1975
ISSN: 0012-365X
DOI: 10.1016/0012-365x(75)90051-5