Computer Science · Graph Theory
Consider the following statements regarding the fundamental properties of tree structures in graph theory: I. A tree is defined as an undirected graph that is both connected and acyclic. II. A tree containing n vertices must have exactly n-1 edges, and adding any new edge to it will create exactly one cycle. III. The removal of any pendant vertex (leaf) from a tree acts as a cut vertex, thereby disconnecting the remaining structure. IV. Every edge in a tree acts as a bridge, meaning the removal of any edge will inevitably disconnect the graph. Choose the most appropriate answer from the options given below:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1I and II Only
- 2II, III and IV Only
- 3I, III and IV Only
- 4I, II and IV Only✓
Correct answer
I, II and IV Only
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