All graphs considered in the paper are directed. Let % be a graph on n vertices which we identify with the elements of the additive cyclic group Zn 1⁄4 f0; 1; . . . ; n 1g. The graph % is called circulant if it has a cyclic symmetry, that is, if the permutation ð0; 1; 2; . . . ; n 1Þ is an automorphism of the graph. Each circulant graph is completely determined by its connection set S which is ...

In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graphG of order n is a Cayley graph over the cyclic groupZn: Equivalently, G is circulant i its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent con guration A and, in particular, a S...

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors. Kwak and Lee (Canad. J. Math. XLII (1990) 747) enumerated the isomorphism classes of graph bundles and those of n-fold coverings with respect to a group of automorphisms of the base graph G which 9x a spanning tree. Hofmeister (Discrete Math. 98 (1991) 175) independently enumerated the isomorphism ...

An n × n matrix D = d[i, j] is said to be circulant, if the entries d[i, j] verifying (j − i) = k mod n, for some k, have the same value (for a survey on circulant matrix properties, see Davis (1979)). A directed (respectively, undirected) graph is circulant, if its adjacency matrix is circulant (respectively, symmetric, and circulant). Similarly, a weighted graph is circulant, if its weighted ...

For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with |i− j| ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedba...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group K o H such that S = a for some a ∈ K with 〈a〉 = K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as ...

The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . , n? 1} and vertices a b are adjacent if gcd(a ? b, n) D, where D Dn, Dn {d : d | n, 1 &lt; n}. Motivated by incorrect proof of previously published result, in this paper we characterize class graphs that strongly regular. More precisely, connected is regular only n composite m d} for some 2.

We show that computing (and even approximating) MAXIMUM CLIQUE and MINIMUM GRAPH COLORING for circulant graphs is essentially as hard as in the general case. In contrast, we show that, under additional constraints, e.g., prime order and/or sparseness, GRAPH ISOMORPHISM and MINIMUM GRAPH COLORING become easier in the circulant case, and we take advantage of spectral techniques for their efficien...