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Determine the edge count of a path complement graph with 14 vertices.

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Determine the edge count of a path complement graph with 14 vertices.

(a) 502

(b) 345

(c) 78

(d) 69

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I need to ask this question from Different Path in a Graph in section Graphs of Discrete Mathematics

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The correct answer is (c) 78

Explanation: Let, an n-path complement graph Pn’ is the graph complement of the path graph Pn. Since Pn is self-complementary, P4’  is isomorphic to P4. Now, Pn’ has an edge count = ^1⁄2(n-2)(n-1). So, the required edge count is=78.

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