Calculating a product of multiple graphs has been studied in mathematics, engineering, computer science, and more recently in network science, particularly in the context of multilayer networks. One of the important questions to be addressed in this area is how to characterize spectral properties of a product graph using those of its factor graphs. While several such characterizations have alre...

Abstract Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching , longest common substring statistics and repeated . Recent lines research focused on extending some these problems vertex-labeled graphs, either by using efficient ad-hoc approaches which do not generalize all input or indexing difficult gra...

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 ...

In this paper we give a full characterization of the idomatic partitions of the direct product of three complete graphs. We also show how to use such a characterization in order to construct idomatic partitions of the direct product of finitely many complete graphs.

In this note, we deal with the characterization of the idomatic partitions and b-colorings of direct products of complete graphs. We recall some known results on idomatic partitions of direct products of complete graphs and we present new results concerning the b-colorings of the direct product of two complete graphs. Finally, some open problems are given.

This note describes fast algorithms for computing the prime factors of connected, nonbipartite graphs with respect to the direct product, and of connected graphs with respect to the strong product. The complexities are O(mmin(n,∆)) for the direct product, and O(ma(G)∆) for the strong, where n is the order of the graph G to be factored, m its size, a(G) its arboricity, and ∆ its maximum degree. ...