Weak-trees with equal distance-2 domination and independent domination

2021 ◽  
Vol 16 (3) ◽  
pp. 101-106
Author(s):  
Guo-Chin Gao ◽  
Min-Jen Jou ◽  
Jenq-Jong Lin
Keyword(s):  
Equal Distance ◽  
Independent Domination

scholarly journals Independent domination in subcubic graphs

2021 ◽  
Author(s):  
A. Akbari ◽  
S. Akbari ◽  
A. Doosthosseini ◽  
Z. Hadizadeh ◽  
Michael A. Henning ◽  
...  
Keyword(s):  
Independent Domination ◽  
Subcubic Graphs

scholarly journals Independence and domination on shogiboard graphs

2017 ◽  
Vol 4 (8) ◽  
pp. 25-37 ◽  
Author(s):  
Doug Chatham
Keyword(s):  
Independence Number ◽  
Domination Number ◽  
The Other ◽  
Independent Domination

Abstract Given a (symmetrically-moving) piece from a chesslike game, such as shogi, and an n×n board, we can form a graph with a vertex for each square and an edge between two vertices if the piece can move from one vertex to the other. We consider two pieces from shogi: the dragon king, which moves like a rook and king from chess, and the dragon horse, which moves like a bishop and rook from chess. We show that the independence number for the dragon kings graph equals the independence number for the queens graph. We show that the (independent) domination number of the dragon kings graph is n − 2 for 4 ≤ n ≤ 6 and n − 3 for n ≥ 7. For the dragon horses graph, we show that the independence number is 2n − 3 for n ≥ 5, the domination number is at most n−1 for n ≥ 4, and the independent domination number is at most n for n ≥ 5.

Transparent Conductive Cu-In-O Thin Films Deposited by Reactive DC Magnetron Sputtering with Different Targets

2011 ◽  
Vol 239-242 ◽  
pp. 2752-2755
Author(s):  
Fan Ye ◽  
Xing Min Cai ◽  
Fu Ping Dai ◽  
Dong Ping Zhang ◽  
Ping Fan ◽  
...  
Keyword(s):  
Thin Films ◽  
Magnetron Sputtering ◽  
Optical Band Gap ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
Dc Magnetron Sputtering ◽  
Flow Rates ◽  
X Ray ◽  
Equal Distance ◽  
Transmittance Curve

Transparent conductive Cu-In-O thin films were deposited by reactive DC magnetron sputtering. Two types of targets were used. The first was In target covered with a fan-shaped Cu plate of the same radius and the second was Cu target on which six In grains of 1.5mm was placed with equal distance between each other. The samples were characterized with scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), UV/VIS spectrophotometer, four-probe measurement etc. SEM shows that the surfaces of all the samples are very smooth. EDX shows that the samples contain Cu, In as well as O, and different targets result in different atomic ratios of Cu to In. A diffraction peak related to rhombohedra-centered In2O3(012) is observed in the XRD spectra of all the samples. For both the two targets, the transmittance decreases with the increase of O2flow rates. The direct optical band gap of all the samples is also estimated according to the transmittance curve. For both the two targets, different O2flow rates result in different sheet resistances and conductivities. The target of Cu on In shows more controllability in the composition and properties of Cu-In-O films.

scholarly journals Hop Domination in Graphs-II

2015 ◽  
Vol 23 (2) ◽  
pp. 187-199
Author(s):  
C. Natarajan ◽  
S.K. Ayyaswamy
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Total Domination ◽  
Minimum Cardinality ◽  
Unicyclic Graphs ◽  
The Family ◽  
Independent Domination ◽  
Domination In Graphs ◽  
Domination Numbers

Abstract Let G = (V;E) be a graph. A set S ⊂ V (G) is a hop dominating set of G if for every v ∈ V - S, there exists u ∈ S such that d(u; v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γh(G). In this paper we characterize the family of trees and unicyclic graphs for which γh(G) = γt(G) and γh(G) = γc(G) where γt(G) and γc(G) are the total domination and connected domination numbers of G respectively. We then present the strong equality of hop domination and hop independent domination numbers for trees. Hop domination numbers of shadow graph and mycielskian graph of graph are also discussed.

On β-Plurality Points in Spatial Voting Games

2021 ◽  
Vol 17 (3) ◽  
pp. 1-21
Author(s):  
Boris Aronov ◽  
Mark De Berg ◽  
Joachim Gudmundsson ◽  
Michael Horton
Keyword(s):  
Spatial Voting ◽  
Voting Games ◽  
Equal Distance ◽  
Alternative Proposal

Let V be a set of n points in mathcal R d , called voters . A point p ∈ mathcal R d is a plurality point for V when the following holds: For every q ∈ mathcal R d , the number of voters closer to p than to q is at least the number of voters closer to q than to p . Thus, in a vote where each  v ∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal  p will not lose against any alternative proposal  q . For most voter sets, a plurality point does not exist. We therefore introduce the concept of β-plurality points , which are defined similarly to regular plurality points, except that the distance of each voter to p (but not to  q ) is scaled by a factor  β , for some constant 0< β ⩽ 1. We investigate the existence and computation of β -plurality points and obtain the following results. • Define β * d := {β : any finite multiset V in mathcal R d admits a β-plurality point. We prove that β * d = √3/2, and that 1/√ d ⩽ β * d ⩽ √ 3/2 for all d ⩾ 3. • Define β ( p, V ) := sup {β : p is a β -plurality point for V }. Given a voter set V in mathcal R 2 , we provide an algorithm that runs in O ( n log n ) time and computes a point p such that β ( p , V ) ⩾ β * b . Moreover, for d ⩾ 2, we can compute a point  p with β ( p , V ) ⩾ 1/√ d in O ( n ) time. • Define β ( V ) := sup { β : V admits a β -plurality point}. We present an algorithm that, given a voter set V in mathcal R d , computes an ((1-ɛ)ċ β ( V ))-plurality point in time O n 2 ɛ 3d-2 ċ log n ɛ d-1 ċ log 2 1ɛ).

Attraction and penetration of Musa by the burrowing nematode, Radopholus similis, in an autotrophic bipartite culture system

Nematology ◽  
2021 ◽  
pp. 1-14
Author(s):  
Suganthagunthalam Dhakshinamoorthy ◽  
Erwin J. Galon ◽  
Annemie Elsen ◽  
Dirk De Waele
Keyword(s):  
Culture System ◽  
Model System ◽  
Radopholus Similis ◽  
Susceptible Plant ◽  
Compartment System ◽  
Female Migration ◽  
Equal Distance ◽  
Burrowing Nematode ◽  
Nematode Chemotaxis

Summary Our objective was to discover the stages (pre- or post-infection) in which the resistance to burrowing nematode (Radopholus similis) occurs in two resistant banana (Musa spp.) cultivars. An autotrophic in vitro culture system was used to compare R. similis migration towards, and penetration into, the banana roots. A new two-compartment autotrophic in vitro model system was developed using agar-based medium to examine the migration of R. similis to either the susceptible ‘Grande Naine’ or the resistant ‘Yangambi km5’ (‘Ykm5’), when both the Musa genotypes were present at equal distance. The autotrophic in vitro model system was advantageous, because it supported continuous root growth due to the actively photosynthesising shoots growing in the open air, while the in vitro root conditions make it possible to observe and assess the nematode chemotaxis in the transparent medium. Significantly fewer nematodes migrated towards the resistant ‘Ykm5’ plants when compared to both the susceptible ‘Grande Naine’, and another resistant cultivar, ‘Saba’, at 1 h after infection. This signals a possibility of a lower concentration or different composition of nematode attractants in ‘Ykm5’ root exudates. No significant differences were observed in the percentage of R. similis that migrated towards the roots of the susceptible and resistant banana plants at 3, 4 and 6 h after inoculation. No significant differences were observed in the percentages of female penetration in the resistant and susceptible plant roots at 1 and 2 days after inoculation. The results of the two-compartment system confirmed that when a choice is given to migrate towards the resistant and susceptible genotypes, no differences were observed in the percentage of female migration towards both the genotypes.

Postface: Brokerage as social practice

2021 ◽  
pp. 092137402110340
Author(s):  
Thomas Bierschenk
Keyword(s):  
Social Practice ◽  
Social Practices ◽  
Ideal Type ◽  
Social Actors ◽  
Classical Definition ◽  
Equal Distance ◽  
Social Type ◽  
Strong Concept

This postface argues for a narrow and analytically strong concept of brokerage, which is oriented towards the classical definition by Boissevain. His ideal type emphasises the agency of brokers who actively pursue their own interests and act at an equal distance to the groups between which they mediate. Furthermore, the text argues for thinking of brokerage as a bundle of social practices instead of as brokers in the sense of a social type. While few social actors are fully-fledged brokers, many of them engage in brokerage.

Independent Domination in Triangle Graphs

2007 ◽  
Vol 28 ◽  
pp. 341-348 ◽  
Author(s):  
Yu.L. Orlovich ◽  
I.E. Zverovich
Keyword(s):  
Independent Domination
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