A Single Formula for Integer Powers of Certain Real Circulant Matrix of Odd and Even Order
نویسندگان
چکیده
In this paper, we derive a single formula for the entries of the rth (r ∈ N) power of a certain real circulant matrix of odd and even order, in terms of the Chebyshev polynomials of the first and second kind. In addition, we give two Maple 13 procedures along with some numerical examples in order to verify our calculation.
منابع مشابه
Fuzzy subgroups of the direct product of a generalized quaternion group and a cyclic group of any odd order
Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I.Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220)proposed the following problem: Find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. In this paper weconsider more general grou...
متن کاملOn the Enumeration of Circulant Graphs of Prime Power and Square Free Orders
The aim of this work is twofold: to unify, systematize and extend the known results of the analytical (i.e. formula-wise) counting of directed and undirected circulant graphs with a prime or, more generally, square-free number of vertices; to develop a general combinatorial framework for the counting of nonisomorphic circulant graphs with pk vertices, p odd prime, k 2. The general problem of co...
متن کاملOn the powers of fuzzy neutrosophic soft matrices
In this paper, The powers of fuzzy neutrosophic soft square matrices (FNSSMs) under the operations $oplus(=max)$ and $otimes(=min)$ are studied. We show that the powers of a given FNSM stabilize if and only if its orbits stabilize for each starting fuzzy neutrosophic soft vector (FNSV) and prove a necessary and sufficient condition for this property using the associated graphs of the FNSM. ...
متن کاملDistance magic circulant graphs
Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, 2, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the open neighborhood of v. In this paper we deal with circulant graphs C(1, p). The circulant graph Cn(1, p) is the graph on the vertex set V = {x0, x1, . . . , xn−1} with edges (xi, xi...
متن کاملRecognizing Recursive Circulant Graphs G(cd M ; D)
Recursive circulant graphs G(N; d) have been introduced in 1994 by Park and Chwa PC94] as a new topology for interconnection networks. Recursive circulant graphs G(N; d) are circu-lant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2 k ; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better param...
متن کامل