Idom.setCSstd.tri {pcds}

The indicator for the set of points S being a dominating set or not for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

Description

Returns I(S a dominating set of the CS-PCD) where the vertices of the CS-PCD are the data set Xp), that is, returns 1 if S is a dominating set of CS-PCD, returns 0 otherwise.

CS proximity region is constructed with respect to the standard equilateral triangle T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2)) with expansion parameter t>0 and edge regions are based on the center M=(m_1,m_2) in Cartesian coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of T_e; default is M=(1,1,1) i.e., the center of mass of T_e (which is equivalent to the circumcenter of T_e).

Edges of T_e, AB, BC, AC, are also labeled as 3, 1, and 2, respectively.

See also (Ceyhan (2012)).

Usage

Idom.setCSstd.tri(S, Xp, t, M = c(1, 1, 1))

Arguments

S

A set of 2D points which is to be tested for being a dominating set for the CS-PCDs.

Xp

A set of 2D points which constitute the vertices of the CS-PCD.

t

A positive real number which serves as the expansion parameter in CS proximity region in the standard equilateral triangle T_e=T((0,0),(1,0),(1/2,\sqrt{3}/2)).

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the standard equilateral triangle T_e; default is M=(1,1,1) i.e. the center of mass of T_e.

Value

I(S a dominating set of the CS-PCD), that is, returns 1 if S is a dominating set of CS-PCD, returns 0 otherwise, where CS proximity region is constructed in the standard equilateral triangle T_e

Author(s)

Elvan Ceyhan

References

Ceyhan E (2012). “An investigation of new graph invariants related to the domination number of random proximity catch digraphs.” Methodology and Computing in Applied Probability, 14(2), 299-334.

See Also

Idom.setCStri and Idom.setPEstd.tri

Examples

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-runif.std.tri(n)$gen.points

M<-as.numeric(runif.std.tri(1)$g)  #try also M<-c(.6,.2)

t<-.5

S<-rbind(Xp[1,],Xp[2,])
Idom.setCSstd.tri(S,Xp,t,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
Idom.setCSstd.tri(S,Xp,t,M)