Computer Science · Graph Theory
Which of the following statements accurately defines the structural relationship between a simple graph and its complement?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The union of a graph and its complement forms a complete graph (Kn), with edges existing in the complement exclusively if they are absent in the original.✓
- 2The union of a graph and its complement forms a complete bipartite graph (Km,n), provided that loops are explicitly included in both structures.
- 3Edges exist in the complement of a graph if and only if they are present in the original graph, resulting in an identical edge count for both.
- 4The union of a graph and its complement forms a null graph, as the complement systematically removes all edges and isolated vertices from the original.
Correct answer
The union of a graph and its complement forms a complete graph (Kn), with edges existing in the complement exclusively if they are absent in the original.
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