On the total vertex irregularity strength of comb product of cycle and path with order 3

Let G = (V (G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f: V (G) boolean OR E(G) -> {1, 2,...,k}. The vertex weight v under the labeling f is denoted by w(f)(v) and defined by w(f)(v) = f(v) + Sigma(uv is an element of E(G)) f(uv). A total k-labeling of G is called vertex irregular if there are no two vertices with the same weight. The total vertex irregularity strength of G, denoted by tvs(G), is the minimum k such that G has a vertex irregular total k-labeling. Let G and H be two connected graphs. Let o be a vertex of H. The comb product between G and H, denoted by G(sic)(o) H, is a graph obtained by taking one copy of G and vertical bar V (G)vertical bar copies of H and grafting the i-th copy of H at the vertex o to the i-th vertex of G. In this paper, we determine the total vertex irregularity strength of comb product of cycle and path with order 3.