The tensor product, also called direct, categorical, or Kronecker product of graphs, is one of the least-understood graph products. In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh (see [2]). We characterize completely those pairs of complete graphs whose tensor products are circulant. We establish that...

It is known that regular digraphs of degree d, diameter k and unique walks of length not smaller than h and not greater than k between all pairs of vertices ([ h, k ]-digraphs), exist only for h k and h = k 1, if d ;::: 2. This paper deals with the problem of the enumeration of [k 1, kJ-digraphs in the case of diameter k = 2 or degree d = 2. It is shown, using algebraic techniques, that the lin...

A natural digraph analogue of the graph-theoretic concept of an ‘independent set’ is that of an ‘acyclic set’, namely a set of vertices not spanning a directed cycle. Hence a digraph analogue of a graph coloring is a decomposition of the vertex set into acyclic sets and we say a digraph is uniquely n-colorable when this decomposition is unique up to relabeling. It was shown probabilistically in...

Let $R$ be a commutative ring. In this paper, by using algebraic properties of $R$, we study the Hase digraph of prime ideals of $R$.

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...

We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order n is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.

We present the results concerning the embedding of trees into recursive circulants. Recursive circulant G(N,:,/) is a circulant graph with N vertices and jumps of powers of d. We present dilation 1 embedding of Fibonacci trees and full quaternaly trees in G(Z”, 2), and full binary trees and hinomial trees in G(2”,4).