For graphs G and H let GH] be their lexicographic product and let f (G) = inff(GK n ])=n j n = 1; 2; : : :g be the fractional chromatic number of G. For n 1 set G n = fG j (GK n ]) = nn(G)g. Then lim n!1 G n = fG j f (G) = (G)g: Moreover, we prove that for any n 2 the class G n forms a proper subclass of G n?1. As a by-product we show that if G is a-extremal, vertex transitive graph on (G)(G) ?...

TshwaneLex is the world's only lexicography software suite with which the entire lexicographic process, from initial compilation all the way to final product, may be conducted in the language of one's choice. This is possible thanks to various aspects of internationalisation, localisation and customisation that are built into TshwaneLex. These are discussed by means of examples drawn from a wid...

We study the behavior of generic initial ideals with respect to fibre products. In our main result we determine the generic initial ideal of the fibre product with respect to the reverse lexicographic order. As an application we compute the symmetric algebraic shifted complex of two disjoint simplicial complexes as was conjectured by Kalai. This result is the symmetric analogue of a theorem of ...

A graph G is an efficient open domination graph if there exists a subset D of V (G) for which the open neighborhoods centered in vertices of D form a partition of V (G). We completely describe efficient domination graphs among direct, lexicographic and strong products of graphs. For the Cartesian product we give a characterization when one factor is K2 and some partial results for grids, cylind...

Magda (1980) and Hedayat (1981) first considered the construction of circular strongly balanced repeated measurements designs. Sen and Mukerjee (1987) and Roy (1988) considered the optimality and existence of circular strongly balanced repeated measurements designs based on the method of differences and Hamiltonian decomposition of lexicographic product of two graphs. In this article, we consid...

The theory of domination in graphs is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology.Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. In this paper, we consider lexicographic product gr...

In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exac...

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. ...

An edge coloring of a graph G with colors 1, 2, . . . , t is called an interval t-coloring if for each i ∈ {1, 2, . . . , t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let N be the set of all i...