The (Strong) Rainbow Connection Number of Join Of Ladder and Trivial Graph

Let G = (V,E) be a nontrivial, finite, and connected graph. A function c from E to {1,2,...,k},k ∈ N, can considered as rainbow k-coloring if every two vertices x y in has an x- path. Therefore, no path's edges receive the same color; this condition is called “rainbow path”. The smallest positive integer k, designated by rc(G), connection number. Thus, k-coloring. Meanwhile, strong within for have - path whose length distance between y. such G, k-coloring; number of denoted src(G). In research, are determined graph resulting join operation ladder trivial graph, rc(L_n∨K_1) src(L_n∨K_1) respectively. So, rc (L_n∨K_1 )= src )=2,"for" 3≤n≤4 )=3, while src(L_n∨K_1 )=⌈n/2⌉,"for" n≥5.