The existence of perfect state transfer in quantum spin networks based on integral circulant graphs has been considered recently by Saxena, Severini and Shparlinski. Motivated by the mentioned work, Bašić, Petković and Stevanović give the simple condition for the characterization of integral circulant graphs allowing the perfect state transfer in terms of its eigenvalues. They stated that integ...

Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...

We propose new families of graphs which exhibit quantum perfect state transfer. Our constructions are based on the join operator on graphs, its circulant generalizations, and the Cartesian product of graphs. We build upon the results of Bašić and Petković (Applied Mathematics Letters 22(10):1609-1615, 2009) and construct new integral circulants and regular graphs with perfect state transfer. Mo...

The integral circulant graph Xn(D) has the vertex set Zn = {0, 1, 2, . . . , n − 1} and vertices a and b are adjacent, if and only if gcd(a − b, n) ∈ D, where D = {d1, d2, . . . , dk} is a set of divisors of n. These graphs play an important role in modeling quantum spin networks supporting the perfect state transfer and also have applications in chemical graph theory. In this paper, we deal wi...

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...

1 Abstract In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graph G of order n is a Cayley graph over the cyclic group Z n : Equivalently, G is circulant ii its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent connguration A and, in...

Let G be a graph with adjacency matrix A. The transition matrix of G relative to A is defined by H(t) := exp (−itA), where t ∈ R. The graph G is said to admit pretty good state transfer between a pair of vertices u and v if there exists a sequence of real numbers {tk} and a complex number γ of unit modulus such that lim k→∞ H(tk)eu = γev. We find that the cycle Cn as well as its complement Cn a...