Super local edge anti-magic total coloring of paths and its derivation

Abstract

Suppose G ( V,E) be a connected simple graph and suppose u,v,x be vertices of graph G. A bijection f : V ∪ E → {1,2,3,...,| V ( G)| + | E ( G)|} is called super local edge antimagic total labeling if for any adjacent edges uv and vx, w ( uv) 6= w ( vx), which w ( uv) = f ( u)+ f ( uv)+ f ( v) for every vertex u,v,x in G, and f ( u) f ( e) for every vertex u and edge e ∈ E ( G). Let γ( G) is the chromatic number of edge coloring of a graph G. By giving G a labeling of f, we denotes the minimum weight of edges needed in G as γ leat ( G). If every labels for vertices is smaller than its edges, then it is be considered γ sleat ( G). In this study, we proved the γ sleat of paths and its derivation.