dc.contributor.author LASIM, Ahmad dc.contributor.author HALIKIN, Ikhsanul dc.contributor.author WIJAYA, Kristiana dc.date.accessioned 2023-02-22T01:48:39Z dc.date.available 2023-02-22T01:48:39Z dc.date.issued 2022-12-15 dc.identifier.uri https://repository.unej.ac.id/xmlui/handle/123456789/112293 dc.description.abstract Suppose 𝐺 is a simple and connected graph with 𝑞 edges. A harmonious labeling on a graph 𝐺 is an injective en_US function 𝑓: 𝑉(𝐺) → {0, 1, 2, … , 𝑞 − 1} so that there exists a bijective function 𝑓 ∗ : 𝐸(𝐺) → {0,1, 2, … , 𝑞 − 1} where 𝑓 ∗(𝑢𝑣) = 𝑓(𝑢) + 𝑓(𝑣)(𝑚𝑜𝑑 𝑞), for each 𝑢𝑣 ∈ 𝐸(𝐺). An odd harmonious labeling on a graph 𝐺 is an injective function 𝑓 from 𝑉(𝐺) to non-negative integer set less than 2𝑞 so that there is a function 𝑓 ∗(𝑢𝑣) = 𝑓(𝑢) + 𝑓(𝑣) where 𝑓 ∗(𝑢𝑣) ∈ {1, 3, 5, … , 2𝑞 − 1} for every 𝑢𝑣 ∈ 𝐸(𝐺). An even harmonious labeling on a graph 𝐺 is an injective function 𝑓: 𝑉(𝐺) → {0, 1, 2, … , 2𝑞} so that there is a bijective function 𝑓 ∗ : 𝐸(𝐺) → {0,2,4, … , 2𝑞 − 2} where 𝑓 ∗(𝑢𝑣) = 𝑓(𝑢) + 𝑓(𝑣)(𝑚𝑜𝑑 2𝑞) for each 𝑢𝑣 ∈ 𝐸(𝐺). In this paper, we discuss how to build new labeling (harmonious, odd harmonious, even harmonious) based on the existing labeling (harmonious, odd harmonious, even harmonious). dc.language.iso en en_US dc.publisher Barekeng en_US dc.subject even harmonious labeling en_US dc.subject harmonious labeling en_US dc.subject odd harmonious labeling en_US dc.title The Harmonious, Odd Harmonious, And Even Harmonious Labeling en_US dc.type Article en_US
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