Search results for "Digraph"

The minimum size of fully irregular oriented graphs

2001

Abstract Digraphs in which any two vertices have different pairs of semi-degrees are called fully irregular. For n-vertex fully irregular oriented graphs (i.e. digraphs without loops or 2-dicycles) the minimum size is presented.

A smallest irregular oriented graph containing a given diregular one

2004

AbstractA digraph is called irregular if its vertices have mutually distinct ordered pairs of semi-degrees. Let D be any diregular oriented graph (without loops or 2-dicycles). A smallest irregular oriented graph F, F=F(D), is constructed such that F includes D as an induced subdigraph, the smallest digraph being one with smallest possible order and with smallest possible size. If the digraph D is arcless then V(D) is an independent set of F(D) comprising almost all vertices of F(D) as |V(D)|→∞. The number of irregular oriented graphs is proved to be superexponential in their order. We could not show that almost all oriented graphs are/are not irregular.

Extremal Irregular Digraphs

2018

A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum sizes among irregular n-vertex whether digraphs or oriented graphs are the same and are asymptotic to (√2/3) n3/2; maximum sizes, however, are asymptotic to n2 and n2/2, respectively. Let s stand for the sum of initial positive integers, s = 1, 3, 6, . . . . An oriented graph Hs and a digraph Fs, both large (in terms of the size), minimal irregular, and on any such s vertices, s ≥ 21, are constructed in [Large minimal irregular digraphs, Op…

Global functorial hypergestures over general skeleta for musical performance

2016

Musical performance theory using Lagrangian formalism, inspired by physical string theory, has been described in previous research. That approach was restricted to zero-addressed hypergestures of local character, and also to digraph skeleta of simple arrow type. In this article, we extend the theory to hypergestures that are defined functorially over general topological categories as addresses, are global, and are also defined for general skeleta. We also prove several versions of the important Escher Theorem for this general setup. This extension is highly motivated by theoretical and practical musical performance requirements of which we give concrete examples.

Uzdevumi sākumskolas skolēnu angļu valodas izrunas pilnveidei

2020

Izruna ir nozīmīga angļu valodas apguves daļa. Izrunas prasmes ietekmē spēju radīt skaņas, saprast valodu un uztvert teiktā nozīmi, kas ir būtiski faktori, lai veidotu veiksmīgu komunikāciju. Šī iemesla dēļ sākumskolas angļu valodas stundās vairāk uzmanības būtu jāvelta izrunas uzlabošanas vingrinājumiem. Izvēloties vingrinājumus, nepieciešams ņemt vērā izrunas apguves īpatnības jaunākā skolas vecuma skolēniem. Lai noteiktu metožu un vingrinājumu efektivitāti izrunas prasmju uzlabošanai sākumskolā, tika pielietotas divas mācību metodes, audiolingvālā mācību metode un tiešā metode, Tukuma 2. vidusskolas 4. klases skolēnu angļu valodas stundās. Noslēguma diagnosticējošais tests apstiprināja, …

Degree sequences of digraphs with highly irregular property

1998

Some properties of vertex-oblique graphs

2016

The type t G ( v ) of a vertex v ? V ( G ) is the ordered degree-sequence ( d 1 , ? , d d G ( v ) ) of the vertices adjacent with v , where d 1 ? ? ? d d G ( v ) . A graph G is called vertex-oblique if it contains no two vertices of the same type. In this paper we show that for reals a , b the class of vertex-oblique graphs G for which | E ( G ) | ? a | V ( G ) | + b holds is finite when a ? 1 and infinite when a ? 2 . Apart from one missing interval, it solves the following problem posed by Schreyer et?al. (2007): How many graphs of bounded average degree are vertex-oblique? Furthermore we obtain the tight upper bound on the independence and clique numbers of vertex-oblique graphs as a fun…