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Nuris Hisan Nazula
University of Jember
Computer Science & IT Decision Sciences, Operations Research & Management

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Local antimagic vertex coloring of unicyclic graphs Nuris Hisan Nazula; S Slamin; D Dafik
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (206.369 KB) | DOI: 10.19184/ijc.2018.2.1.4

Abstract

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.
Co-Authors D. Dafik S Slamin