Nilai ketakteraturan refleksif titik pada graf Petersen diperumum P(n, 2)

Maharani, Astrini Fitriani (2021) Nilai ketakteraturan refleksif titik pada graf Petersen diperumum P(n, 2). Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

INDONESIA: Untuk suatu graf G, misalkan ρ adalah pelabelan-k total pada graf tersebut. Didefinisikan pelabelan-k total sehingga sisi pada G diberi label bilangan bulat {1,2,…,k_e } dan titik pada G diberi label bilangan bulat genap {0,2,…,〖2k〗_v }, dimana k=max{k_e,〖2k〗_v }. Bobot titik u adalah penjumlahan label titik u dan semua label sisi yang terkait dengan titik u yang dinotasikan dengan 〖wt〗_ρ (u), didefinisikan sebagai 〖wt〗_ρ (u)=ρ(u)+∑_(uv∈E(G))▒〖ρ(uv)〗. Pelabelan-k total dikatakan sebagai pelabelan-k refleksif tak teratur titik jika untuk u,v∈V(G), 〖wt〗_ρ (u)≠〖wt〗_ρ (v). Nilai k terkecil sehingga graf G memiliki pelabelan-k refleksif tak teratur titik disebut nilai ketakteraturan refleksif titik pada graf G, dinotasikan dengan rvs(G). Penelitian ini membahas nilai ketakteraturan refleksif titik pada graf Petersen diperumum P(n, 2), dinotasikan dengan rvs(P(n, 2)). ENGLISH: For a graph G, let ρ be the total-k labeling of the graph. Defined total-k labeling such that the edges of G are labeled with integers {1,2,…,k_e } and the vertices of G are labeled with even integers {0,2,…,〖2k〗_v }, where k=max{k_e,〖2k〗_v }. The weight of a vertex u is the sum of the label of vertex u and the labels of all edges incident vertex u denoted by 〖wt〗_ρ (u), defined as 〖wt〗_ρ (u)=ρ(u)+∑_(uv∈E(G))▒〖ρ(uv)〗. The total-k labeling is called a vertex irregular reflexive k-labeling if for u,v∈V(G), 〖wt〗_ρ (u)≠〖wt〗_ρ (v). The minimum k for which a graph G has a vertex irregular reflexive k-labeling is called the reflexive vertex irregularity strength of G, denoted by rvs(G). This research discusses the reflexive vertex irregularity strength of generalized Petersen graph P(n, 2), denoted by rvs(P(n, 2)).

Item Type: Thesis (Sarjana)
Uncontrolled Keywords: Pelabelan-k refleksif tak teratur titik; nilai ketakteraturan refleksif titik; graf Petersen diperumum; vertex irregular reflexive k-labeling, reflexive vertex irregularity strength, generalized Petersen graph.
Subjects: Mathematics
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Astrini Fitriani Maharani
Date Deposited: 20 Aug 2021 01:52
Last Modified: 20 Aug 2021 01:52
URI: https://digilib.uinsgd.ac.id/id/eprint/42029

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