Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph

Abstract

: Let 𝜒(cid:4666)𝐺(cid:4667) be a chromatic number of vertex coloring of a graph G. A bijection 𝑓: 𝐸 → (cid:4668)1,2,3, … ,|𝐸(cid:4666)𝐺(cid:4667)|(cid:4669) is called local antimagic vertex coloring if for any adjacent vertices do not share the same weight, where the weight of a vertex in 𝐺 is the sum of the label of edges incident to it. We denote the minimum number of distinct weight of vertices in 𝐺 so that the graph 𝐺 admits a local antimagic vertex coloring as 𝜒 (cid:3039)(cid:3028) (cid:4666)𝐺(cid:4667) . In this study, we established the missing value of 𝜒 (cid:3039)(cid:3028) for a case in wheel graph and 𝜒 (cid:3039)(cid:3028) for helm graph.