On the vertex local antimagic total labeling chromatic number of $G\odot {K}_{2}$

Kurniawati, Elsa Yuli; Agustin, Ika Hesti; Dafik, Dafik; Marsidi, Marsidi

doi:10.1088/1742-6596/1211/1/012018

Cited by 3 publications

(2 citation statements)

References 2 publications

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“…Putri et al [11] initiated a variation of local antimagic coloring named local antimagic total vertex labeling where the label is assigned to the vertices and edges of G. The weight of vertex u ∈ V , w(u), is the sum of labels of all edges incident with u and the label of u itself. A local antimagic total chromatic number of G, denoted by χ lat (G), is the minimum number of colors induced by local vertex antimagic total labeling of G. The local antimagic total chromatic number of some graphs have been discovered such as star, a double star, banana tree, centipede, amalgamation of graphs [11] and the corona product of some graphs with K 2 [7].…”

Section: Introductionmentioning

confidence: 99%

On local antimagic vertex coloring of corona products related to friendship and fan graph

Himami

Silaban

2021

IJC

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Let G=(V,E) be connected graph. A bijection f : E → {1,2,3,..., |E|} is a local antimagic of G if any adjacent vertices u,v ∈ V satisfies w(u)≠ w(v), where w(u)=∑e∈E(u) f(e), E(u) is the set of edges incident to u. When vertex u is assigned the color w(u), we called it a local antimagic vertex coloring of G. A local antimagic chromatic number of G, denoted by χla(G), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of G. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on m vertices, namely, χla(Fn ⊙ \overline{K_m}) and χla(f(1,n) ⊙ \overline{K_m}).

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Section: Introductionmentioning

confidence: 99%

On local antimagic vertex coloring of corona products related to friendship and fan graph

Himami

Silaban

2021

IJC

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“…Arumugam et al introduced local antimagic as vertex local antimagic edge labelings [3]. Followed by labels addition for the vertex, vertex local antimagic total labelings, one described in by Kurniawati et al [8]. The analog rises, edge local antimagic total labelings, explained by Agustin et al in [1] that includes path graph.…”

Section: Introductionmentioning

confidence: 99%

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

Hadiputra

Silaban

Maryati³

2020

IJC

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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 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.

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The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

Yang

Bian

et al. 2022

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Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u and v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), and E(u) is the set of edges incident to u. Thus, any local antimagic total labeling induces a proper coloring of G, where the vertex x in G is assigned the color ωt(x). The local antimagic total chromatic number, denoted by χlat(G), is the minimum number of colors taken over all colorings induced by local antimagic total labelings of G. In this paper, we present the local antimagic total chromatic numbers of some wheel-related graphs, such as the fan graph Fn, the bowknot graph Bn,n, the Dutch windmill graph D4n, the analogous Dutch graph AD4n and the flower graph Fn.

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On the vertex local antimagic total labeling chromatic number of $G\odot {K}_{2}$

Cited by 3 publications

References 2 publications

On local antimagic vertex coloring of corona products related to friendship and fan graph

On local antimagic vertex coloring of corona products related to friendship and fan graph

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

The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

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