A path on n vertices, P n , is a graph with vertices that can be labeled v 1, v 2, v 3 , v n , so that there is an edge between v 1 and v 2 , between v 2 and v 3 , between v 3 and v 4 , , and between v n1 and v n For example, the graph P 5 appears in Figure 8 22 Compute (P 5 ) Compute (P 6 ) Comput...

A path on n vertices, P n , is a graph with vertices that can be labeled

Question:

A path on n vertices, P_n, is a graph with vertices that can be labeled v_1, v_2, v₃,.... v_n, so that there is an edge between v₁ and v₂, between v₂ and v₃, between v₃ and v₄, . . . , and between v_n–1and v_n. For example, the graph P₅ appears in Figure 8.22. Compute β(P₅). Compute β(P₆). Compute β(P_n) (your answer should be a function of n).