Idom.setCStri {pcds}

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

Description

Returns I(S a dominating set of CS-PCD whose vertices 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 triangle tri with the 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 the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri.

The triangle tri=T(A,B,C) has edges AB, BC, AC which are also labeled as edges 3, 1, and 2, respectively.

See also (Ceyhan (2012)).

Usage

Idom.setCStri(S, Xp, tri, 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.

tri

A 3 \times 2 matrix with each row representing a vertex of the triangle.

t

A positive real number which serves as the expansion parameter in CS proximity region constructed in the triangle tri.

M

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

Value

I(S a dominating set of the CS-PCD), that is, returns 1 if S is a dominating set of CS-PCD whose vertices are the data points in Xp; returns 0 otherwise, where CS proximity region is constructed in the triangle tri

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.setCSstd.tri, Idom.setPEtri and Idom.setAStri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10

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

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

tau<-.5
S<-rbind(Xp[1,],Xp[2,])
Idom.setCStri(S,Xp,Tr,tau,M)

S<-rbind(Xp[1,],Xp[2,],Xp[3,],Xp[5,])
Idom.setCStri(S,Xp,Tr,tau,M)