21、(2, 3)-Cordial Graphs: Resolving Conjectures and Exploring Hypercubes

(2, 3)-Cordial Graphs: Resolving Conjectures and Exploring Hypercubes

1. Resolution of Two Conjectures

• Conjecture 1
  • Statement : Every orientation of every path is (2, 3) cordial except for a path with four vertices.
  • Verification : A brute - force algorithm was used to test if a certain arc orientation is cordial on a friendly labeling of a graph. The algorithm steps are as follows:

Data: Arcs, Verticies
Result: Determine if an orientation is cordial on a path
for arc in Arcs  do
    current = first vertex
    next = second vertex
    if arc is left then
        edgeLabel = current - next
    end
    else