The study of combinatorial properties of finite point configurations is a vast area of research in geometry, whose origins go back at least to the ancient Greeks. Since it includes virtually all problems starting with “consider a set of n points in space,” space limitations impose the necessity of making choices. As a result, we will restrict our attention to Euclidean spaces and will discuss p...

In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we giv...

We prove that the incidence chromatic number of every 3-degenerated graph G is at most ∆(G)+ 4. It is known that the incidence chromatic number of every graph G with maximum average degree mad(G) < 3 is at most ∆(G)+3. We show that when ∆(G) ≥ 5, this bound may be decreased to ∆(G) + 2. Moreover, we show that for every graph G with mad(G) < 22/9 (resp. with mad(G) < 16/7 and ∆(G) ≥ 4), this bou...

In this paper, the concept of incidence domination number of graphs  is introduced and the incidence dominating set and  the incidence domination number  of some particular graphs such as  paths, cycles, wheels, complete graphs and stars are studied.

the robust coloring problem (rcp) is a generalization of the well-known graph coloring problem where we seek for a solution that remains valid when extra edges are added. the rcp is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. this problem has been proved as np-hard and in instances larger than 30 vertices, meta-...

We introduce colorings and orientations of matrices as generalizations of the graph theoretic terms. The permanent per(A[ζ|ξ]) of certain copies A[ζ|ξ] of a matrix A can be expressed as a weighted sum over the orientations or the colorings of A . When applied to incidence matrices of graphs these equations include Alon and Tarsi’s theorem about Eulerian orientations and the existence of list co...