Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

The chromatic number of G× H can be less than the minimum of the chromatic numbers of
finite simple graphs G and H. The tensor product G× H of finite simple graphs G and H has …

Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there
exists some shortest u− w path containing v or some shortest v− w path containing u. A set W …

The thinness of a graph is a width parameter that generalizes some properties of interval
graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be …

The direct product G× H of graphs G and H is defined by and In this paper, we will prove that
holds for all vertex-transitive graphs G and H, which provides an affirmative answer to a …

One of the most famous conjectures in graph theory is Hedetniemi's conjecture stating that
the chromatic number of the categorical product of graphs is the minimum of their chromatic …

We introduce the concept of the primitivity of independent set in vertex‐transitive graphs,
and investigate the relationship between the primitivity and the structure of maximum …

The problem of uniquely recognizing the position of an intruder in a network was the
principal motivation of introducing the concept of metric generators in graphs by Slater in …

Our purpose is to show that complements of line graphs (of graphs) enjoy nice coloring
properties. We show that for all graphs in this class the local and usual chromatic numbers …

A clique-colouring of a graph G is a colouring of the vertices of G so that no maximal clique
of size at least two is monochromatic. The clique-hypergraph, H (G), of a graph G has V (G) …