This paper provides further results on the perfect state transfer in integral circulant graphs (ICG graphs). The non-existence of PST is proved for several classes of ICG graphs containing an isolated divisor d0, i.e. the divisor which is relatively prime to all other divisors from d ∈ D \ {d0}. The same result is obtained for classes of integral circulant graphs having the NSF property (i.e. e...

It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the diameter and the average distance of the graph on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural to...

Abstract We compute the determinant of a matrix containing Ramanujan sums associated to divisors an integer n , and use this computation prove weak version So’s conjecture on circulant graphs with integral spectrum.

A graph G is a prime distance graph (respectively, a 2-odd graph) if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is prime (either 2 or odd). We prove that trees, cycles, and bipartite graphs are prime distance graphs, and that Dutch windmill graphs and paper mill graphs are prime distance graphs if and only if the Tw...

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...

Abstract We study the invariance of KMS states on graph $C^{\ast }$ -algebras coming from strongly connected and circulant graphs under classical quantum symmetry graphs. show that unique state for is invariant automorphism group graph. For graphs, it shown action groups preserves only one occurring at critical inverse temperature. also give an example a -algebra having more than such all them ...

In 2006, Danielsen and Parker [8] proved that every self-dual additive code over GF (4) is equivalent to a graph code. So, graph is an important tool for searching (proposed) optimum codes. In this paper, we introduce a new method of searching (proposed) optimum additive codes from circulant graphs. AMS Subject Classification 2010: 94B05, 05C50, 05C25.

Effective solutions to problems encountered in networks are often based on whether the elementary set can be partitioned into classes according to some specific criteria. The chromatic number of a graph G(V,E) is the minimum number of colours needed to colour the vertices of G such that no two adjacent vertices have the same colour. An independent set D of G is called an efficient dominating se...