(Similarity) Domination Numbers in Graphs Resulting from Shackle Operations with Linkage of any Graph

Saifudin, Ilham and Widiyaningtyas, Triyanna and Rohmad, Wahid and Dasuki, Moh. (2024) (Similarity) Domination Numbers in Graphs Resulting from Shackle Operations with Linkage of any Graph. Universitas Muhammadiyah Mataram.

Text 2024-03-30 [ Similarity ] [ Domination Numbers in Graphs Resulting from Shackle Operations with Linkage of any Graph ].pdf - Other Download (1MB)

Abstract

The domination number is the number of dominating nodes in a graph that can dominate the surrounding connected nodes with a minimum number of dominating nodes. This domini number is denoted by γ(G). In this research, we will examine the domination number of the distance between two graphs resulting from the shackle operation with any graph as linkage. This differs from previous research, namely the domination of numbers at one and two distances. This study emphasizes how the results of operations on the shackle are connected to the shackle graph as any graph connects the copy. Any graph here means all graphs are connected and generally accepted. The method used in this research is pattern recognition and axiomatic deductive methods. The pattern detection method examines patterns where a graph's number of dominating points can dominate the connected points around it with a minimum number of dominating nodes. Meanwhile, axiomatic deductive is a research method that uses the principles of deductive proof that apply to mathematical logic by using existing axioms or theorems to solve a problem. The Result of graph �� with � copies and �� as linkage, then the two-distance domination number in the graph resulting from the shackle operation is ��(�����(��,��,�) )=�−�; graph �� with � copies and �� as linkage, then the two-distance domination number in the graph resulting from the shackle operation is ��(�����(��,��,�) )={�,��� �≤�≤�⌈��⌉(�−�),��� �≥�; graph �� with � copies and �� as linkage, then the two-distance domination number in the graph resulting from the shackle operation is
�2(�ℎ���(��,��,�) )={�−1,��� �=3�,��� 4≤�≤5⌈�5⌉�,��� �≥6
This research provides benefits and adds to research results in the field of graph theory specialization of two-distance domination numbers in the result graph of shackle operation with linkage any graph.

Contribution

Nama Dosen Pembimbing

NIDN/NIDK

Author

Saifudin, Ilham

nidn0731108903

Item Type:	Peer Review
Keywords/Kata Kunci:	Domination Number; Shackle Operation; Result Graph; Any Graph as Linkage.
Subjects:	500 Natural Science and Mathematics > 510 Mathematics > 518 Numerical Analysis
Divisions:	Faculty of Engineering > Department of Informatics Engineering (S1)
Depositing User:	Dasuki Moh | moh.dasuki22@unmuhjember.ac.id
Date Deposited:	07 Mar 2025 03:00
Last Modified:	07 Mar 2025 03:00
URI:	http://repository.unmuhjember.ac.id/id/eprint/24503

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