Answer to Question #222067 in Discrete Mathematics for Sach

Question

Branches and chords may change according to the spanning tree.”-- Do you agree? Justify your answer

Answer 1

Solution:

A tree is a connected graph without cycles.

A tree T is said to be a spanning tree of a connected graph G if T is a subgraph of G which spans over all vertices of G.

An edge in a spanning tree T is called a branch.

An edge of G which is not present in the given spanning tree T of G is called a chord.

Let's take an example of the following spanning tree:

Dark lines show branches, while light ones denote chords.

Here we can see that if we change spanning tree, it will surely change braches and chords. For instance, remove b₁, we get different spanning tree and thus number of braches and chords will be changed.