MathDB

S,T

are two trees without vertices of degree 2. To each edge is associated a positive number which is called length of this edge. Distance between two arbitrary vertices

v,w

in this graph is defined by sum of length of all edges in the path between

v

and

w

. Let

f

be a bijective function from leaves of

S

to leaves of

T

, such that for each two leaves

u,v

S

, distance of

u,v

S

is equal to distance of

f(u), f(v)

T

. Prove that there is a bijective function

g

from vertices of

S

to vertices of

T

such that for each two vertices

u,v

S

, distance of

u,v

S

is equal to distance of

g(u)

and

g(v)

T

Problem Statement