Let \(G\) be a graph with 100! vertices, with each vertex labelled by a…

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 = _____.