GATE | GATE CS 2018 | Question 56

Let G be a graph with 100! vertices, with each vertex labelled by a distinct permutation of the numbers 1, 2, ..., 100. There is an edge between vertices u and v if and only if the label of u can be obtained by swapping two adjacent numbers in the label of v. Let y denote the degree of a vertex in G, and z denote the number of connected components in G. Then y + 10z = _______ . 

Note -This was Numerical Type question.

(A)

(B)

(C)

(D)