Local Edge Antimagic Coloring of Graphs

Agustin, Ika Hesti; Hasan, Moh.; Dafik, Dafik; Alfarisi, Ridho; Prihandini, R. M.

doi:10.17654/ms102091925

Cited by 40 publications

(19 citation statements)

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“…Arumugam et al [5] give a lower bound and upper bound of local antimagic vertex colouring of 1 + and also give the exact value of local antimagic vertex colouring. 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: 99%

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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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Section: Remark 11 For Any Graph Gmentioning

confidence: 99%

“…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: 99%

The local antimagic on disjoint union of some family graphs

Marsidi

Agustin

2019

JMM

Self Cite

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“…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. If every vertex labels are smaller than edge labels, then it is a super local edge antimagic total labelings, which Agustin et al [2] and Kurniawati et al [7] describe in some other 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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“…Local edge antimagic coloring developed from local antimagic vertex coloring of graph G. Agustin et al [1] studied the existence of local edge antimagic coloring of some special graphs. By local edge antimagic coloring, we mean a bijection f : V (G) −→ {1, 2, ..., |V (G)|} is called a local edge antimagic coloring if for any two incident edges at the same vertices e 1 and e 2 , w(e 1 ) = w(e 2 ), where for e = uv ∈ G, w(e) = f (u) + f (v).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, any local edge antimagic labeling induces a proper edge coloring of G if each edge e is assigned the color w(e). The local edge antimagic chromatic number of graph G denoted by γ lea (G) [1].…”

Section: Introductionmentioning

confidence: 99%