Circulants, inversion of circulants, and some related matrix algebras
نویسندگان
چکیده
منابع مشابه
Permanents of Circulants: A Transfer Matrix Approach
Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixed-jump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by ...
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The line graph of G, denoted L(G), is the graph with vertex set E(G), where vertices x and y are adjacent in L(G) iff edges x and y share a common vertex in G. In this paper, we determine all graphs G for which L(G) is a circulant graph. We will prove that if L(G) is a circulant, then G must be one of three graphs: the complete graph K4, the cycle Cn, or the complete bipartite graph Ka,b, for s...
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A graph G is stable if its normalized chromatic difference sequence is equal to the normalized chromatic di erence sequence of G G, the Cartesian product of G with itself. Let be the independence number of G and ! be its clique number. Suppose that G has n vertices. We show that the rst ! terms of the normalized chromatic di erence sequence of a stable graph G must be =n; and further that if G ...
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We study families of integer circulant matrices and methods for determining which are unimodular. This problem arises in the study of cyclically presented groups, and leads to the following problem concerning polynomials with integer coefficients: given a polynomial f(x) ∈ Z[x], determine all those n ∈ N such that Res(f(x), xn − 1) = ±1. In this paper we describe methods for resolving this prob...
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A multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular polyhedra, suns, and cylinders can be analyzed using this scheme.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1984
ISSN: 0024-3795
DOI: 10.1016/0024-3795(84)90111-3