A note on t $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{r}$$ cá-

A note on dimers and T-graphs

The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation between the dimer model on the heaxgonal lattice with a given slope, and the behaviour of the uniform spanning tree on the associated T-graph. Together with the main result of the companion paper [1], the results here sho...

A note on extending t-designs

Khosrovshahi and Ajoodani-Namini a new method for extend-"-U"'.) with k t + L Teirlinck sets with the same TUI'!"~.n'lI"t:,pr~ their results to any k a different method. In this paper, we t + 1 and construct a of large sets of dis

A Note on t-designs with t Intersection Numbers

Let X be a finite set of v elements, called points, and let β be a finite family of distinct k-subsets of X , called blocks. Then the pair D = (X ,β) is called a t-design with parameters (v,k,λ) if any t-subset of X is contained in exactly λ members of β. If λi denotes the number of blocks containing i points, i = 0,1,2, . . . , t−1, then λi is independent of the choice of the i points and λi (...

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

A note on potentially K1, 1, t-graphic sequences