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

Fawwaz Fakhrurrozi Hadiputra, Denny Riama Silaban, Tita Khalis Maryati

#### Abstract

Suppose G(V,E) be a connected simple graph and suppose u,v,x be vertices of graph G. A bijection f : VE → {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 eE(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 γleat(G). If every labels for vertices is smaller than its edges, then it is be considered γsleat(G). In this study, we proved the γ sleat of paths and its derivation.

#### Keywords

Edge chromatic number; Path graphs; Super local edge antimagic; Total coloring

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#### References

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DOI: http://dx.doi.org/10.19184/ijc.2019.3.2.6

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ISSN: 2541-2205

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