Amalgamations and Cycle-Antimagicness

Xiong, Yijun; Wang, Huajun; Habib, Mustafa; Umar, Muhammad Awais; Ali, Basharat Rehman

doi:10.1109/access.2019.2936844

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…On the other hand, its edge labeling is based on the Equation ( 6), (7), and (8). So, the total of edge label for each 𝐶 𝑛 𝑖 , when 𝑖 is even, is This proves that for 𝑡 even number, 𝐴𝑚𝑎𝑙{𝐶 𝑛 } 𝑡 admits a super (𝑎, 𝑑)-𝐶 𝑛 -antimagic decomposition.…”

Section: Proofmentioning

confidence: 88%

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Magic and Antimagic Decomposition of Amalgamation of Cycles

Pancahayani¹,

Soemarsono²,

Adzkiya³

et al. 2022

Advances in Computer Science Research

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Consider 𝐺 = (𝑉, 𝐸) as a finite, simple, connected graph with vertex set 𝑉 and edge set 𝐸. 𝐺 is said to be a decomposable graph if there exists a collection of subgraphs of 𝐺, say ℋ = {𝐻 𝑖 |1 ≤ 𝑖 ≤ 𝑛} such that for every 𝑖 ≠ 𝑗, 𝐻 𝑖 is isomorphic to 𝐻 𝑗 , ⋃ 𝐻 𝑖 𝑛 𝑖=1 = 𝐺 and should satisfy that 𝐸(𝐻 𝑖 ) ∩ 𝐸(𝐻 𝑗 ) = ∅ if 𝑖 ≠ 𝑗. Let 𝑓: 𝑉(𝐺) ∪ 𝐸(𝐺) → {1,2, … , |𝑉(𝐺)| + |𝐸(𝐺)|} be a bijection mapping such that every subgraph in ℋ has the same total of valuation 𝑤(𝐻 𝑖 ) = ∑(𝑓(𝑣) + 𝑓(𝑒)) = 𝑘 for 𝑣 ∈ 𝑉(𝐻 𝑖 ) and 𝑒 ∈ 𝐸(𝐻 𝑖 ). In this paper, 𝑘 is called a magic constant. If every subgraph 𝐻 𝑖 ≅ 𝐻 and using this labelling results 𝑤(𝐻 𝑖 ) = 𝑘 for all 𝑖, then 𝐺 admits 𝐻-magic decomposition. Otherwise, if the total values among all subgraphs are different, then 𝐺 admits 𝐻-antimagic decomposition. In this research, a graph derived from amalgamating some cycles in a terminal vertex is the object to be investigated to find its property regarding magic decomposition. Furthermore, we find that the vertex amalgamation of some identical cycles admits both magic and antimagic decomposition, which depends on its order.

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Section: Proofmentioning

confidence: 88%

“…On the other hand, Inayah et al in [6] studied magic and antimagic decomposition for complete graphs, and Hendy et al in [7] explained how to decompose antimagically toroidal grids and triangulations. Specifically, Xiong et al in [8] worked and observed the amalgamation of wheels, fans, and flower graphs.…”

Section: Introductionmentioning

confidence: 99%

Magic and Antimagic Decomposition of Amalgamation of Cycles

Pancahayani¹,

Soemarsono²,

Adzkiya³

et al. 2022

Advances in Computer Science Research

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“…Recent results on H-antimagic labeling of graphs can be seen in [8][9][10][11][12][13][14]. Also, in [12], Baca et al discussed the tree-antimagicness of disconnected graphs. Recently, authors in [15] discussed the super (a, 1)-tree-antimagicness of Sun graphs.…”

Section: Introductionmentioning

confidence: 99%

H-Coverings of Path-Amalgamated Ladders and Fans

Xiong

Wang

Umar³

et al. 2020

Mathematical Problems in Engineering

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Let G be a connected, simple graph with finite vertices v and edges e . A family G 1 , G 2 , … , G p ⊂ G of subgraphs such that for all e ∈ E , e ∈ G l , for some l , l = 1,2 , … , p is an edge-covering of G . If G l ≅ ℍ , ∀ l , then G has an ℍ -covering. Graph G with ℍ -covering is an a d , d - ℍ -antimagic if ψ : V G ∪ E G ⟶ 1,2 , … , v + e a bijection exists and the sum over all vertex-weights and edge-weights of ℍ forms a set a d , a d + d , … , a d + p − 1 d . The labeling ψ is super for ψ V G = 1,2,3 , … , v and graph G is ℍ -supermagic for d = 0 . This manuscript proves results about super ℍ -antimagic labeling of path amalgamation of ladders and fans for several differences.

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Radio Labeling for Strong Product K₃ ⊠ P_n

Nazeer

Kousar

et al. 2020

IEEE Access

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Many variations of graph labeling has been defined in the literature. e.g., graceful, harmonious and radio labeling etc. In information technology and in data sciences, we need secrecy of data, different channel assignment and accuracy of transmission of the data. This make the use of graph terminologies indispensable for the computer programs. In this paper, we will discuss multi-distance radio labeling used for channel assignment problem over a wireless communication. A radio (multidistance) labeling of a graph G is a function h from V (G) to the set of non-negative integers such that |h(u)−h(v)| ≥ diam(G)+1−d G (u, v) ,Where diam(G) and d G (u, v) are diameter and distance between u and v in graph G respectively. The span of a radio labeling h is the maximum integer assigned by h and radio number of a graph G is the minimum span taken over all radio labeling of G. In this article, we will find relations for radio number of a strong product K 3 P n , n ≥ 3.

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Amalgamations and Cycle-Antimagicness

Cited by 3 publications

References 13 publications

Magic and Antimagic Decomposition of Amalgamation of Cycles

Magic and Antimagic Decomposition of Amalgamation of Cycles

H-Coverings of Path-Amalgamated Ladders and Fans

Radio Labeling for Strong Product K₃ ⊠ P_n

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Amalgamations and Cycle-Antimagicness

Cited by 3 publications

References 13 publications

Magic and Antimagic Decomposition of Amalgamation of Cycles

Magic and Antimagic Decomposition of Amalgamation of Cycles

H-Coverings of Path-Amalgamated Ladders and Fans

Radio Labeling for Strong Product K3 ⊠ Pn

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Product

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Radio Labeling for Strong Product K₃ ⊠ P_n