Tardif, C., Prefibers and the Cartesian product of metric spaces, Discrete Mathematics 109 (1992) 283-288. The properties of certain sets called prefibers in a metric space are used to show that the algebraic properties of the Cartesian product of graphs generalize to metric spaces.

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspect...

Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole. Consider a single player game in which a robot or obstacle can be moved to adjacent vertex if it has a hole. The objective is to take the robot to a fixed destination vert...

let g be a simple connected graph. the generalized polarity wiener index ofg is defined as the number of unordered pairs of vertices of g whosedistance is k. some formulas are obtained for computing the generalizedpolarity wiener index of the cartesian product and the tensor product ofgraphs in this article.

In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube of dimension n, Hamming graph, C4 nanotubes, nanotorus, grid, t−fold bristled, sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

We present some results on the growth in various products of graphs. In particular we study the Cartesian, strong, lexicographic, tensor and free product of graphs. We show that with respect to distances the tensor product behaves differently from other products. In general the results are valid for rooted graphs but have especially nice structure in the case of vertex-transitive factors.

A clique minor in a graph G can be thought of as a set of connected subgraphs in G that are pairwise disjoint and pairwise adjacent. The Hadwiger number η(G) is the maximum cardinality of a clique minor in G. It is one of the principle measures of the structural complexity of a graph. This paper studies clique minors in the Cartesian product G H. Our main result is a rough structural characteri...

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...

A partition of V (G), all of whose classes are dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic number of G. The concept of a domatic number was introduced in [1]. More interesting results on domatically full graphs, domatically critical, domatically cocritical graphs and other domatic numbers can be found ...