Bilangan Dominasi Pada Graf Sierpinski S(n,C4)

Suhendra, Rikcy Bayu (2019) Bilangan Dominasi Pada Graf Sierpinski S(n,C4). Masters thesis, Institut Teknologi Sepuluh Nopember.

Text 06111650012015-Master_Thesis.pdf - Accepted Version Restricted to Repository staff only until 1 October 2022. Download (15MB) | Request a copy

Abstract

Himpunan dominasi S pada graf G=(V,E)$adalah subset dari V sedemikian hingga setiap simpul yang bukan elemen S terhubung dan berjarak satu terhadap S. Kardinalitas minimum dari himpunan dominasi pada pada graf G disebut bilangan dominasi dari graf G dan dinotasikan gamma (G). Sedangkan himpunan Dominasi sisi D pada Graf G adalah subset dari E(G) sedemikian hingga setiap sisi yang bukan elemen D terhubung dan berjarak satu terhadap D. Dari definisi dasar diatas tanpa mengurangi keumuman berlaku untuk bilangan dominasi berjarak l, yang dinotasikan dengan gamma l. Kardinalitas minimum himpunan dominasi sisi pada Graf G disebut bilangan dominasi sisi dari Graf G dan dinotasikan gamma '(G). Dalam penelitian ini ditentukan bilangan dominasi sisi dan simpul pada Graf Sierspinki In-m, Graf Sierspinki 4-Cycle In-m, Sierspinki 4-Cycle Diag In-m}. Hasil dari bentuk umum bilangan dominasi pada Graf Sierspinki In-m memiliki minimum 2^{2n-1} , bilangan dominasi Graf Sierpinski 4-Cycle In-m memiliki minimum 2^{2n-2} ,bilangan dominasi Graf Sierpinski 4-Ccycle Diag In-m memiliki minimum 2^{2n-2} katakunci :Bilangan Dominasi, Graf Sierpinski In-m, Himpunan Dominasi, Graf Sierpinski 4-Cycle In-m,Graf Sierpinski 4-Cycle Diag In-m}}
================================================================================================
Dominating set S in the graph G = (V, E) is a subset of V such that
each vertex G that is not element S is connected and have distance as one
to S. The minimum cardinality from dominating sets on graph G was called
dominating number of graph G and denoted γ(G). Dominating set D in the
graph G is a subset of E(G) such that each edge G that is not element D
is connected and have distance as one to D. From elementary definition,
without loss of generallity give for dominating number l distance, denoted by
γl The minimum cardinality between dominating sets on graph G was called
dominating edge number of graph G and denoted γ′(G). In this study, we
determined l distanced dominating number on Sierspinki graph S(n, C4) by
inserting m vertex on each edge smallest fractal graph C4, for further we found
relation and general formula of dominating set obtained. The result showed
that dominating number on Sierspinki graph In-m have a minimum 22n−1 ,
dominating number on Sierspinki graph 4-Cycle In-m have a minimum 22n−2
,dominating number on Sierspinki graph 4-Cycle Diag In-m have a minimum
22n−2

Item Type:	Thesis (Masters)
Additional Information:	RTMa 511.5 Suh b-1 2019
Uncontrolled Keywords:	Dominating Number, Sierpinski Graph In-m,Sierpinski Graph 4-Cycle In-m, Sierpinski Graph 4-Cycle Diag In-m Dominating Set i
Subjects:	Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Rikcy Bayu Suhendra
Date Deposited:	26 Jan 2022 03:01
Last Modified:	26 Jan 2022 03:02
URI:	http://repository.its.ac.id/id/eprint/62101

Actions (login required)

View Item