On the Study of Rainbow Antimagic Connection Number of Comb Product of Friendship Graph and Tree

Given a graph G with vertex set V(G) and edge E(G), for the bijective function f(V(G))?{1,2,?,|V(G)|}, associated weight of an xy?E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, called edge-antimagic labeling. A path P in vertex-labeled said to be rainbow x?y if every two xy,x?y??E(P) it satisfies w(xy)?w(x?y?). The antimagic labeling there exists vertices x,y?V(G). We say that admits coloring when we assign each xy color w(xy). smallest number colors induced from weights connection G, denoted by rac(G). This paper intended investigate non-symmetrical phenomena comb product graphs considering optimizing connection, coloring. In this paper, show exact value Fn?Tm, where Fn friendship order 2n+1 Tm?{Pm,Sm,Brm,p,Sm,m}, Pm m, Sm star m+1, Brm,p broom m+p Sm,m double 2m+2.