# GATE Papers >> CSE >> 2018 >> Question No 53

Question No. 53
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 = _____.