(a) Show that for any vertices x,y,z in a graph G,
dist(x,z)<=dist(x,y)+dist(y,z).
(b) Recall that the diameter of a graph G is the longest possible distance between any two vertices in G.
Recall that the n cube, Q_(n) is the graph whose vertices are binary strings with n digits, and two vertices
are adjacent if they differ in exactly one digit. Show that for all positive integers n,
diameter (Q_(n))=n.
Include an example of two vertices that are distance n from each other.
1.
(a) Show that for any vertices x,y,z in a graph G,
dist(x,z)< dist(x,y)+dist(y,z)
b) Recall that the diameter of a graph G is the longest possible distance between any two vertices in G Recall that the n cube, Qn is the graph whose vertices are binary strings with n digits, and two vertices are adjacent if they differ in exactly one digit. Show that for all positive integers n,
diameter(Qn)=n.
Include an example of two vertices that are distance n from each other