Every graph has only one minimum spanning tree. State true or false.a)Falseb)True

The statement "Every graph has only one minimum spanning tree" is False.

Explanation:

1. Multiple Minimum Spanning Trees: A graph can have more than one minimum spanning tree if there are edges with the same weight. For instance, in a graph where multiple edges connecting the same vertices are of equal minimum weight, different combinations of these edges can yield different spanning trees that all have the same total weight.

2. Counterexample: Consider a triangle graph with vertices A, B, and C, where the edges AB, AC, and BC all have the same weight (e.g., weight = 1). Here, you can choose any two edges as a spanning tree, leading to multiple minimum spanning trees.

Thus, the correct answer is:

Final Answer

a) False