2022
DOI: 10.1080/09720529.2021.1892270
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On local antimagic chromatic number of spider graphs

Abstract: Let G = (V, E) be a connected simple graph. A bijection f :holds for any two adjacent vertices u and v, where f + (u) = e∈E(u) f (e) and E(u) is the set of edges incident to u. A graph G is called local antimagic if G admits at least a local antimagic labeling. The local antimagic chromatic number, denoted χ la (G), is the minimum number of induced colors taken over local antimagic labelings of G. Let G and H be two disjoint graphs. The graph G[H] is obtained by the lexicographic product of G and H. In this pa… Show more

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Cited by 3 publications
(10 citation statements)
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References 11 publications
(12 reference statements)
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“…, a s ), is a tree formed by identifying an end-vertex, called the core vertex, of each path of length a i for each 1 ≤ i ≤ s, where 1 ≤ a 1 ≤ • • • ≤ a s . In [7], the authors obtained many sufficient conditions so that χ la (Sp(a 1 , a 2 , . .…”
Section: From Spider Graphsmentioning
confidence: 99%
See 2 more Smart Citations
“…, a s ), is a tree formed by identifying an end-vertex, called the core vertex, of each path of length a i for each 1 ≤ i ≤ s, where 1 ≤ a 1 ≤ • • • ≤ a s . In [7], the authors obtained many sufficient conditions so that χ la (Sp(a 1 , a 2 , . .…”
Section: From Spider Graphsmentioning
confidence: 99%
“…So we only consider s ≥ 3. From the proof of [7,Theorem 2.11], the core vertex has the induced color q, all vertices of degree 2 are labelled by q or q + 1, where q is the size of the spider graph. Now we merge all pendant vertices.…”
Section: From Spider Graphsmentioning
confidence: 99%
See 1 more Smart Citation
“…Consequently, we showed that χ la (f n • O m ) = m(2n + 1) + 2 for n ≥ 2, m = 1. Interested readers may refer to [9][10][11][12] for local antimagic chromatic number of graphs with pendant edges.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, Sp(2 [n] ) is the spider graph with n legs of length 2. A spider graph is also know as a one point union of at least three paths at an end vertex (see [4]). Note that Sp(2 [n] ) is known as the amalgamation of n copies of P 3 at a pendant vertex, denoted Amal(P 3 , x, n) in [5], where x is the degree n vertex of Sp(2 [n] ).…”
Section: Introductionmentioning
confidence: 99%