2022
DOI: 10.2991/acsr.k.220202.011
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Magic and Antimagic Decomposition of Amalgamation of Cycles

Abstract: 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 β„‹ = {𝐻 𝑖 |1 ≀ 𝑖 ≀ 𝑛} such that for every 𝑖 β‰  𝑗, 𝐻 𝑖 is isomorphic to 𝐻 𝑗 , ⋃ 𝐻 𝑖 𝑛 𝑖=1 = 𝐺 and should satisfy that 𝐸(𝐻 𝑖 ) ∩ 𝐸(𝐻 𝑗 ) = βˆ… if 𝑖 β‰  𝑗. Let 𝑓: 𝑉(𝐺) βˆͺ 𝐸(𝐺) β†’ {1,2, … , |𝑉(𝐺)| + |𝐸(𝐺)|} be a bijection mapping such that every subgraph in β„‹ has the same total of valuation 𝑀(𝐻 𝑖 ) = βˆ‘(οΏ½… Show more

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