Local antimagic vertex coloring of unicyclic graphs

Nuris Hisan Nazula, S Slamin, D Dafik


The local antimagic labeling on a graph G with ∣V∣ vertices and ∣E∣ edges is defined to be an assignment f : E → {1, 2, ⋯, ∣E∣} so that the weights of any two adjacent vertices u and v are distinct, that is, w(u) ≠ w(v) where w(u) = Σe ∈ E(u)f(e) and E(u) is the set of edges incident to u. Therefore, any local antimagic labeling induces a proper vertex coloring of G where the vertex u is assigned the color w(u). The local antimagic chromatic number, denoted by χla(G), is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we present the local antimagic chromatic number of unicyclic graphs that is the graphs containing exactly one cycle such as kite and cycle with two neighbour pendants.


local antimagic labeling; vertex coloring; unicyclic graphs; kite

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DOI: http://dx.doi.org/10.19184/ijc.2018.2.1.4


S. Arumugam, K.Premalatha, M. Baca, A. Semanicova-Fenovcikova, Local antimagic vertex coloring of a graph, Graph and Combinatorics 33 (2017) 275-285.

W. D. Wallis, E. T. Baskoro, Mirka Miller and Slamin, Edge-magic total labeling, Australasian Journal of Combinatorics 22 (2000) 177-190.

L. Cai and J.A. Ellis, Edge colouring line graphs of unicyclic graphs, Discrete Applied Math- ematics 36 (1992) 75-82.

A.S. Pedersen and P.D. Vestergaard, The number of independent sets in unicyclic graphs, Discrete Applied Mathematics 152 (2005) 246-256.


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