Let G=(V, E) be a connected, undirected and simple graph. For k ∈ N, let w : E(G) → {1, 2, ···, k} be an integer edge-weighting of a graph G. An edge-weighting w induces a vertex coloring f_w : V(G) → N defined by f_w(v) = Σ_(v∈e) w(e). An edge-weighting is called vertex coloring if f_w(u) ≠ f_w(v) for any edge uv, denoted by μ(G). The minimum k for which G has a vertex-coloring k-edge-weighting. In this paper, our results include lower bound of vertex coloring edge weighting of G + K_1 and the exact value of vertex coloring edge-weighting of some wheel related graphs include fan, friendship, wheel, helm, flower, sun folwer, and closed helm graph.
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