Domination in certain chemical graphs

Quadras, Jasintha; Mahizl, A.S.M.; Rajasingh, Indra; Rajan, R. Sundara

doi:10.1007/s10910-014-0422-1

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…Figure 7 illustrates R 4,3 . The last class of pericondensed hexagonal systems that we focus on in this paper was introduced by Quadras et al [14].…”

Section: Prolate Rectangle R Nmmentioning

confidence: 99%

Domination and Independent Domination in Hexagonal Systems

Almalki

Kaemawichanurat

2021

Mathematics

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A vertex subset D of G is a dominating set if every vertex in V(G)∖D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge. The domination number γ(G) of a graph G is the minimum cardinality of a dominating set of G, and the independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. A classical work related to the relationship between γ(G) and i(G) of a graph G was established in 1978 by Allan and Laskar. They proved that every K1,3-free graph G satisfies γ(G)=i(H). Hexagonal systems (2 connected planar graphs whose interior faces are all hexagons) have been extensively studied as they are used to present bezenoid hydrocarbon structures which play an important role in organic chemistry. The domination numbers of hexagonal systems have been studied continuously since 2018 when Hutchinson et al. posted conjectures, generated from a computer program called Conjecturing, related to the domination numbers of hexagonal systems. Very recently in 2021, Bermudo et al. answered all of these conjectures. In this paper, we extend these studies by considering the relationship between the domination number and the independent domination number of hexagonal systems. Although every hexagonal system H with at least two hexagons contains K1,3 as an induced subgraph, we find many classes of hexagonal systems whose domination number is equal to an independent domination number. However, we establish the existence of a hexagonal system H such that γ(H)<i(H) with the prescribed number of hexagons.

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“…Figure 7 illustrates R 4,3 . The last class of pericondensed hexagonal systems that we focus on in this paper was introduced by Quadras et al [14].…”

Section: Prolate Rectangle R Nmmentioning

confidence: 99%

Domination and Independent Domination in Hexagonal Systems

Almalki

Kaemawichanurat

2021

Mathematics

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“…The Domination number and the bondage number for pyrene torus, Balaban 10cage is obtained in Domination in certain graphs [8]. The domination number, the total domination number and the connected domination number for some chemical graphs is obtained in [9].…”

Section: Brief Survey On Application Of Chemical Graph Theorymentioning

confidence: 99%

Roman Domination of Some Chemical Graphs

Sangolli

Gudgeri

Varsha

et al. 2021

JPRI

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The concept of Domination in graphs has application to the study of DNA structures. For investigating the chemical and physical properties, several topological indices used are Wiener index, Randic index, Zagreb index, Kier & Hall index that depends on vertex degree and distance sum, and have been used extensively for QSAR and QSPR studies. A Roman Dominating Function of G is function f: V→ {0, 1, 2} such that every vertex v for which f (v) = 0 has a neighbor u with f(u) = 2. The weight of a Roman dominating function f is w (f) = . The Roman domination number of a graph G is denoted by (G) and is the minimum weight of all possible Roman dominating functions. In this paper, we find Roman domination number of some chemicals graphs such as saturated hydrocarbons and unsaturated hydrocarbons, hexagonal chain, pyrene, Hexabenzocoronene, H-Phenylenic nanotube and N-Napthelenic nanotube.

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“…There are a lot of parameters had been studied since domination in graphs is being discovered. Several applications have been contributed by the concept of domination such as finding the optimum solution in social network theory [8], protection and location strategies [9], and chemical bond problems [10] [11], among others [12] [13] [14].…”

Section: Introductionmentioning

confidence: 99%

A Note on Triple Repetition Sequence of Domination Number in Graphs

Casinillo

Ocampo

2022

InPrime:Ind.Jour.Pure.Applied.Math

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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

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Domination in certain chemical graphs

Cited by 18 publications

References 17 publications

Domination and Independent Domination in Hexagonal Systems

Domination and Independent Domination in Hexagonal Systems

Roman Domination of Some Chemical Graphs

A Note on Triple Repetition Sequence of Domination Number in Graphs

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