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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics
Emily L. Casinillo
Department of Mathematics, Visayas State University, Visca, Baybay City, Leyte
Computer Science & IT Mathematics

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A Note on Triple Repetition Sequence of Domination Number in Graphs Leomarich F. Casinillo; Emily L. Casinillo; Lanndon A. Ocampo
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 2 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i2.24573

Abstract

A set D subset of V(G) is a dominating set of a graph G if for all x ϵ V(G)\D, for some y ϵ D such that xy ϵ E(G). A dominating set D subset of V(G) is called a connected dominating set of a graph G if the subgraph <D> induced by D is connected. A connected domination number of G, denoted by γ_c(G), is the minimum cardinality of a connected dominating set D. The triple repetition sequence denoted by {S_n:n ϵ Z+} is a sequence of positive integers which is repeated thrice, i.e., {S_n}={1,1,1,2,2,2,3,3,3, ...}. In this paper, we construct a combinatorial explicit formula for the triple repetition sequence of connected domination numbers of a triangular grid graph.Keywords: connected domination number; triangular grid graph; triple repetition sequence. AbstrakSuatu himpunan D subhimpunan dari V(G) adalah himpunan pendominasi graf G apabila untuk semua x ϵ V(G)\D, untuk suatu y ϵ D sehingga xy ϵ E(G). Suatu himpunan pendominasi D subhimpunan dari V(G) dikatakan himpunan pendominasi terhubung dari graf G apabila subgraf <D> yang diinduksi oleh D terhubung. Suatu bilangan pendominasi dari G, dinotasikan dengan γ_c(G), adalah kardinalitas minimum dari himpunan pendominasi terhubung D. Barisan pengulangan rangkap tiga yang dinotasikan dengan {S_n:n ϵ Z+} adalah suatu barisan bilangan bulat positif yang setiap sukunya berulang tiga kali, yakni, {S_n}={1,1,1,2,2,2,3,3,3, ...}. Dalam paper ini dikonstruksi suatu rumus eksplisit kombinatorial untuk barisan pengulangan rangkap tiga dari bilangan pendominasi terhubung graf grid triangular.Kata Kunci: bilangan pendominasi terhubung; graf grid triangular; barisan pengulangan rangkap tiga. 2020MSC: 05C69
Co-Authors Lanndon A. Ocampo Leomarich F. Casinillo