1. Let graph G = (V, E) be a directed graph with no loops (no edge of type (u, u)) or parallel edges (if (u, v) is an edge then (v, u) can not be an edge). The degree of a vertex v in G is defined as the number of vertices that are at (shortest path) distance one from v. Similarly, second-degree of v the number of vertices that are at distance two from v. Prove that if minimum degree of G is eight(8) then there must exist a vertex with degree less than or equal to its second-degree, i.e., J u V, |N(u)SIUvEN() N(u) \ N()|. (20)