Question

For every tree there will be ______ number of cut set matrices.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Hint:

Remember the unique one-to-one mapping rule in graph topology: One specific tree $\rightarrow$ exactly 1 Fundamental Cut-Set Matrix ($\mathbf{Q}_f$) and exactly 1 Fundamental Tie-Set Matrix ($\mathbf{B}_f$).

Answer 1

The Correct Option is A

Understanding the Concept: In network graph theory:
• A Tree is a connected subgraph of an overall main electrical network graph containing all nodes of the parent graph but containing absolutely no closed loops or internal circuits.
• The branches that comprise the chosen tree are designated as twigs. If a graph has $N$ total nodes, any valid tree contains exactly $n = (N - 1)$ twigs.
• A Fundamental Cut-Set is formed by choosing exactly one single tree twig along with a specific set of remaining links (chords). Step-by-step Structural Breakdown:
• Since each fundamental cut-set must contain exactly one unique twig from the chosen tree, the total number of fundamental cut-sets that can be formed matches the number of available twigs: $$\text{Number of Fundamental Cut-sets} = N - 1$$
• By systematically organizing these specific fundamental cut-sets as row vectors, we construct the Fundamental Cut-Set Matrix (conventionally denoted as $\mathbf{Q}_f$).
• For any uniquely selected single tree configuration inside a graph, there is only one specific, well-defined set of fundamental cut-sets that satisfies this structural criteria.
• Consequently, for every defined tree choice, there exists exactly one unique fundamental cut-set matrix.