In this paper, we investigate spectral norms for circulant-type matrices, including circulant, skewcirculant and g-circulant matrices. The entries are product of binomial coefficients with Fibonacci numbers and Lucas numbers, respectively. We obtain identity estimations for these spectral norms. Employing these approaches, we list some numerical tests to verify our results.

We explore ways to concisely describe circulant graphs, highly symmetric graphs with properties that are easier to generalize than other graphs. We introduce connection sets as a way to describe isomorphism among some circulant graphs and discuss Ádám’s conjecture that attempts to generalize this idea to all circulant graphs, exploring cases in which the conjecture holds and cases in which it f...

In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.

In this paper, it is considered a g-circulant, right circulant, left circulant and a special kind of tridiagonal matrices whose entries are h(x)-Fibonacci polynomials. The determinant of these matrices is established and with the tridiagonal matrices we show that the determinant is equal to the nth term of the h(x)-Fibonacci polynomials.

Enumerating the isomorphism classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory (see [R. Feng, J.H. Kwak, J. Kim, J. Lee, Isomorphism classes of concrete graph coverings, SIAM J. Discrete Math. 11 (1998) 265–272; R. Feng, J.H. Kwak, Typical circulant double coverings of a circulant graph, Discrete Math. 277 (2004) 73–85; R. F...

This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound k = O(ǫ log(n)) for Gaussian circulant JL embeddings. Moreo...

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 circulant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better paramete...

In this paper, a necessary and sufficient condition for the existence of an efficient 2-dominating set in a class of circulant graphs has been obtained and for those circulant graphs, an upper bound for the 2domination number is also obtained. For the circulant graphs Cir(n,A), where A = {1, 2, . . . , x, n − 1, n − 2, . . . , n − x} and x ≤ bn−1 2 c, the perfect 2-tuple total domination number...

In this paper, we discuss the solutions to a class of Hermitian positive deenite system Ax = b by the preconditioned conjugate gradient method with circulant preconditioner C. In general, the smaller the condition number (C ?1=2 AC ?1=2) is, the faster the convergence of the method will be. The circulant matrix C b that minimizes (C ?1=2 AC ?1=2) is called the best conditioned circulant precond...

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...