GATE CS 2014 Set 2 — Question 61
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Engineering Mathematics → Graph Theory (Math) → Graph Terminology (Degree, Paths, Cycles)
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Question
A cycle on vertices is isomorphic to its complement. The value of is _____.
Correct answer
5 to 5
Solution
A cycle graph has vertices and edges. For a graph to be isomorphic to its complement (self-complementary), it must have exactly half the number of edges of a complete graph on the same number of vertices.
1.The number of edges in a complete graph is given by .
2.For a graph to be self-complementary, its number of edges must satisfy .
3.For a cycle graph , the number of edges is .
4.Equating the two:
Since a cycle must have at least 3 vertices (), the only valid solution is .Continue learning with Success Tracker
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