Gate 2018 Qn. 43

Question

 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 and if and only if the label of can be obtained by swapping two adjacent numbers in the label of . Let  denote the degree of a vertex in G, and denote the number of connected components in G.  Then, y + 10z = _____.

Comments

https://gateoverflow.in/204117/gate2018-43