Macaulay2 » Documentation
Packages » Graphs :: vertexMultiplication
next | previous | forward | backward | up | index | toc

vertexMultiplication

Description

Multiplying the vertex of a graph adds one vertex to the original graph. It also adds several edges, namely, if we are multiplying a vertex v and calling the new vertex u, {u,W} is an edge if and only if {v,w} is an edge.

i1 : G = completeGraph 5

o1 = Graph{0 => {1, 2, 3, 4}}
           1 => {0, 2, 3, 4}
           2 => {0, 1, 3, 4}
           3 => {0, 1, 2, 4}
           4 => {0, 1, 2, 3}

o1 : Graph
i2 : H = vertexMultiplication(G, 0, 6)

o2 = Graph{0 => {1, 2, 3, 4}   }
           1 => {0, 2, 3, 4, 6}
           2 => {0, 1, 3, 4, 6}
           3 => {0, 1, 2, 4, 6}
           4 => {0, 1, 2, 3, 6}
           6 => {1, 2, 3, 4}

o2 : Graph

Ways to use vertexMultiplication:

  • vertexMultiplication(Graph,Thing,Thing)

For the programmer

The object vertexMultiplication is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Graphs.m2:5243:0.