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

Fawwaz Fakhrurrozi Hadiputra, Denny Riama Silaban, Tita Khalis Maryati


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.


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

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I. H. Agustin, Dafik, Moch. Hasan, R. Alfarisi, and R. M. Prihandini, On the local edge antimagic coloring of graphs, Far East Journal of Mathematical Science 102 (9) (2017) pp. 1925 - 1941.

I. H. Agustin, R. Alfarisi, Dafik, and A. I. Kristiana, On Super Local Antimagic Total Edge Coloring of Some Wheel Related Graphs, AIP Conference Proceedings 2014 (2018) 020088.

S. Arumugam, K. Premalatha, M. Baˇ ca, and A. Semanicova-Fenovcikova, Local antimagic vertex coloring of a graph, Graphs Combin. 33 (2017) pp. 275-285.

R. Bodendiek and G. Walther, On arithmetic antimagic edge labelings of graphs, Mitt. Math.Ges. Hamburg 17 (1998) pp. 85-99.

J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics 21 (2018) DS6.

N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, San Diego (1990).

E. Y. Kurniawati, I. H. Agustin, Dafik, and R. Alfarisi, Super local edge antimagic total coloring of PnH, IOP Conf. Series: Journal of Physics: Conf. Series 1008 (2018) 012036 pp. 1-11.

E. Y. Kurniawati, I. H. Agustin, Dafik, and Marsidi, On the vertex local antimagic total labeling chromatic number of GK2 , IOP Conf. Series: Journal of Physics: Conf. Series 1211 (2019) 012018 pp. 1-8.


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