On super (a,d)-antimagic total covering of star related graphs

Kathiresan, K.; Laurence, S. David

doi:10.7151/dmgt.1832

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2022

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“…In this paper, a partial solution is obtained to an open problem posed by Kathiresan and David Laurencea [9]. First, the graph G u [S n ], n is even, has no super (a, p + q + 2)-G + e-antimagic total labeling is proved.…”

Section: Conclusion and Scopementioning

confidence: 97%

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Super (a, d)-G + e-antimagic total labeling of Gᵤ[Sn]

Rajkumar

Nalliah

Maheswari

2022

Proyecciones (Antofagasta)

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Let G = (V, E) be a simple graph and H be a subgraph of G. Then G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection ƒ : V (G) ∪ E(G) → {1, 2, 3, ..., |V (G)| + |E(G)|} such that for all subgraphs H’ of G isomorphic to H, the H’ weights w(H’) =∑v∈V(H’) f(v) + =∑e∈E(H’) f(e) constitute an arithmetic progression {a, a + d, a + 2d, ..., a + (n − 1)d}, where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. The labeling ƒ is called a super (a, d)-H-antimagic total labeling if ƒ (V (G)) = {1, 2, 3, ..., |V (G)|}. In [9], authors have posed an open problem to characterize the super (a, d)-G+ e-antimagic total labeling of the graph Gu[Sn], where n ≥ 3 and 4 ≤ d ≤ p+q + 2. In this paper, a partial solution to this problem is obtained.

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Section: Conclusion and Scopementioning

confidence: 97%

“…In [9], they investigated the super (a, d)-H-antimagic total labeling of star related graphs G u [S n ] is defined as follows. Let G be a (p, q) graph and S n be a star with n edges.…”

Section: Introductionmentioning

confidence: 99%