On the local antimagic total edge chromatic number of amalgamation of graphs

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

doi:10.1063/1.5054494

Cited by 13 publications

(3 citation statements)

References 3 publications

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“…Agustin et al [6] studied the local edge antimagic colouring of graphs. The other results about local antimagic of graphs can be seen in [6] - [10].…”

Section: Remark 11 For Any Graph Gmentioning

confidence: 95%

The local antimagic on disjoint union of some family graphs

Marsidi

Agustin

2019

JMM

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A graph in this paper is nontrivial, finite, connected, simple, and undirected. Graph consists of a vertex set and edge set. Let u,v be two elements in vertex set, and q is the cardinality of edge set in G, a bijective function from the edge set to the first q natural number is called a vertex local antimagic edge labelling if for any two adjacent vertices and , the weight of is not equal with the weight of , where the weight of (denoted by ) is the sum of labels of edges that are incident to . Furthermore, any vertex local antimagic edge labelling induces a proper vertex colouring on where is the colour on the vertex . The vertex local antimagic chromatic number is the minimum number of colours taken over all colourings induced by vertex local antimagic edge labelling of . In this paper, we discuss about the vertex local antimagic chromatic number on disjoint union of some family graphs, namely path, cycle, star, and friendship, and also determine the lower bound of vertex local antimagic chromatic number of disjoint union graphs. The chromatic numbers of disjoint union graph in this paper attend the lower bound.

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“…Agustin et al [6] studied the local edge antimagic colouring of graphs. The other results about local antimagic of graphs can be seen in [6] - [10].…”

Section: Remark 11 For Any Graph Gmentioning

confidence: 95%

The local antimagic on disjoint union of some family graphs

Marsidi

Agustin

2019

JMM

Self Cite

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“…The local antimagic total chromatic number of G, denoted by χ lat (G), is the minimum number of colors taken over all colorings induced by local antimagic total labelings of G. Clearly, χ la (G) ≥ χ lat (G) ≥ χ(G) for any graph G. Putri et al [10] presented the local antimagic total chromatic numbers of some families tree, such as star, double star, banana tree graph, centipede graph, and the amalgamation of the star graph. In [11], Kurniawati et al determined the exact values of local antimagic total chromatic numbers of graphs G K 2 , when G is the star, path, cycle and friendship graphs. Moreover, Kurniawati et al [12] determined the exact value of graphs G mK 1 , when G is the star, path, cycle and friendship graphs.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], Kurniawati et al determined the exact values of local antimagic total chromatic numbers of graphs G K 2 , when G is the star, path, cycle and friendship graphs. Moreover, Kurniawati et al [12] determined the exact value of graphs G mK 1 , when G is the star, path, cycle and friendship graphs.…”

Section: Introductionmentioning

confidence: 99%

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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