Stacked book graphs are cycle-antimagic

Ma, Xinqiang; Umar, Muhammad Awais; Nazeer, Saima; Chu, Yu‐Ming; You-yuan, Liu

doi:10.3934/math.2020387

Cited by 2 publications

(2 citation statements)

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“…nected graphs. Some graphs belonging to cycle-antimagic graph were given in [4,5,6,7,8]. For more results related to 𝐻 -antimagicness of graphs, one can see [9,10].…”

Section: 𝜑(𝑒)mentioning

confidence: 99%

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On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs

Inayah

Susanto

Semaničová-Feňovčíková

2021

Heliyon

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An (𝑎, 𝑑)-𝐻-antimagic total labeling of a simple graph 𝐺 admitting an 𝐻-covering is a bijection 𝜑 ∶ 𝑉 (𝐺) ∪ 𝐸(𝐺) → {1, 2, … , |𝑉 (𝐺)| + |𝐸(𝐺)|} such that for all subgraphs 𝐻 ′ of 𝐺 isomorphic to 𝐻, the set of 𝐻 ′ -weights given byforms an arithmetic sequence 𝑎, 𝑎 + 𝑑, … , 𝑎 + (𝑡 − 1)𝑑 where 𝑎 > 0, 𝑑 ⩾ 0 are two fixed integers and 𝑡 is the number of all subgraphs of 𝐺 isomorphic to 𝐻. Moreover, such a labeling 𝜑 is called super if the smallest possible labels appear on the vertices. A (super) (𝑎, 𝑑)-𝐻-antimagic graph is a graph that admits a (super) (𝑎, 𝑑)-𝐻-antimagic total labeling. In this paper the existence of super (𝑎, 𝑑)-𝐻-antimagic total labelings for the 𝑚-shadow and the closed 𝑚-shadow of a connected 𝐺 for several values of 𝑑 is proved.Problem 1. For 2 ⩽ 𝑡 ⩽ 𝑚 − 1, determine 𝐷 𝑡 (𝐺)-supermagic labelings for the 𝑚-shadow 𝐷 𝑚 (𝐺) of any connected graph 𝐺 on 𝑝 vertices and 𝑞 edges.

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“…nected graphs. Some graphs belonging to cycle-antimagic graph were given in [4,5,6,7,8]. For more results related to 𝐻 -antimagicness of graphs, one can see [9,10].…”

Section: 𝜑(𝑒)mentioning

confidence: 99%

“…Bača et al in [3] investigated the H -antimagicness of disconnected graphs. Some graphs belonging to cycle-antimagic graph were given in [4] , [5] , [6] , [7] , [8] . For more results related to H -antimagicness of graphs, one can see [9] , [10] .…”

Section: Introductionmentioning

confidence: 99%