BILANGAN DOMINASI-LOKASI HASIL KALI SISIR GRAF LINTASAN DENGAN BEBERAPA GRAF REGULER

Authors

  • Aulia Sibua Universitas Pasifik Morotai
  • Anuwar Kadir Abdul Gafur Universitas Pasifik Morotai

DOI:

https://doi.org/10.55098/amalgamasi.v1.i2.pp71-78

Keywords:

the comb product, the domination set, the location-dominated number

Abstract

To all the paper, all graph is connected, simple, undirected, and finite. A set vertex W of  is called the domination set if every vertex for every  is adjacent to some vertex  The minimum cardinality of a location-dominated set is called the location-dominated number, which is denoted by λ(G). In this research, we observe to the comb product of a path graph to regular graphs. If noticed to the definition of a regular graph, then obtained a complete graph is  graph with order . So in the results of this research we start by looking for the location-dominated number of the comb product of a path graph with a regular graph where the regular graph is a ,  end which each one has , , dan  where order  end .

References

AKA Gafur, Dan A. W. Bustan (2019). "Mengidentifikasi Bilangan Dominasi Lokasi Pada Graf Bintang Kipas". the original of mathematics, Program Studi Matematika, Fakultas FMIPA, Universitas Pasifik Morotai. Media,neliti, 3-8.

A Kadir A Gafur, S W Saputro, On locating-dominating set of regular graph, Journal of mathematics, volume 2021, 6 pages, doi.org/10.1155/2021/8147514

Ignacio M Pelayo, Locating-dominating in graphs, preprint.

J. Caceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, Locating-dominating codes : Bound and extremal cardianities, arXiv:1025.2177v1 [math.CO] 10 Mey 2012.

G. Chartrand, L. Eroh, M. Johnson, dan O. R. Ollerman, resolvabililty in graph and Metric dimension of graph., Discrete Appl. 105, (2000), 99-113.

G. Chartrand, dan P. Zhang, The theory and applications of resolvability in graphs; a survey, 160 (2003), 47-68.

C. Chen, C. Lu, Identifying codes and locating-dominating sets on paths and cycles, arXiv:0908.2750v1 [math.CO] 19 Agu 2009.

F. Harary dan R. A. melter, On the metric dimension of graph, Ars Combin., 2 (1976), 191-195.

T. W. Haynes, S. T. Hedetniemi, dan P. J. Salter, Fundamentals of domination in graphs, Marcel Dekker, New York, 1998.

R. Jayagopal, R. Sundara Rajan, Indra Rajasingh, Tigh lower bound for locating-total dominating number, Internasional Jurnal of Pure and Applied Mathematics, 101 (2015), 661-668.

S. Khuller, B. Raghavachari, dan A. Rosenfeld, Landmarks in graphs, Discrete Appl. Math., 70 (1996), 217-229.

P. J. Salter, Leaves of trees, Congres. Number., 14 (1975), 549559

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Published

2022-11-17

How to Cite

Sibua, A., & Kadir Abdul Gafur, A. (2022). BILANGAN DOMINASI-LOKASI HASIL KALI SISIR GRAF LINTASAN DENGAN BEBERAPA GRAF REGULER. Amalgamasi: Journal of Mathematics and Applications, 1(2), 71–78. https://doi.org/10.55098/amalgamasi.v1.i2.pp71-78