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### Strong equality of domination parameters in trees

Teresa W. Haynes, Michael A. Henning, Peter J. Slater
2003 Discrete Mathematics
We study the concept of strong equality of domination parameters.  ...  A constructive characterization of the trees T for which (T ) = t (T ), where t (T ) denotes the total domination number of T , is also presented.  ...  This motivates the deÿnition of strong equality of parameters (see [3, 4] ).  ...

### Strong Equality of MAJORITY Domination Parameters

J. Joseline Manora, B John
2014 IOSR Journal of Mathematics
We study the concept of strong equality of majority domination parameters.  ...  Let 1 P and 2 P be properties of vertex subsets of a graph, and assume that every subset of () VG with property 2 P also has property 1  ...  If the degree of a vertex v satisfies ( ) 1 2 p dv     , then the vertex () v V G  is called a majority dominating vertex of G. II. Strong equality of Majority domination Parameters.  ...

### On Equality and Strong Equality of Domination Number and Independent Domination Number in Graphs

Pious Femlin, Joseph Mayamma
2015 Mapana Journal of Sciences
In this paper we explore graphs having same domination number and independent domination number . Such graphs are denoted as ( , )-graphs. Several families of ( , )-graphs have been constructed.  ...  Furthermore, properties of graphs in which every -set is a -set has been investigated.  ...  Strong equality between  and i  This section deals with the concept called strong equality of domination number and independent domination number in graphs.  ...

### Global Alliances and Independent Domination in Some Classes of Graphs

Odile Favaron
2008 Electronic Journal of Combinatorics
A dominating set $S$ of a graph $G$ is a global (strong) defensive alliance if for every vertex $v\in S$, the number of neighbors $v$ has in $S$ plus one is at least (greater than) the number of neighbors  ...  The dominating set $S$ is a global (strong) offensive alliance if for every vertex $v\in V\setminus S$, the number of neighbors $v$ has in $S$ is at least (greater than) the number of neighbors it has  ...  They also noticed that for trees T , the independence domination number i is "incomparable" to some global alliance parameters in that sense that i(T ) can be smaller than γ a (T ) or γ o (T ), or greater  ...

### DOMINATION AND EDGE DOMINATION IN TREES

B. Senthilkumar, Yanamandram B. Venkatakrishnan, H. Naresh Kumar
2020 Ural Mathematical Journal
We characterize trees with domination number equal to twice edge domination number.  ...  The domination number of a graph $$G$$, denoted by $$\gamma(G)$$ is the minimum cardinality of a dominating set of $$G$$.  ...  Acknowledgements The authors thank the anonymous referees for their helpful and constructive comments leading to improvements in the presentation of the paper.  ...

### Page 1494 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews
parameters are equal for inflated trees.  ...  We provide a constructive characterisation of those trees with equal domination and restrained domination numbers.  ...

### Hop Domination in Graphs-II

C. Natarajan, S.K. Ayyaswamy
2015 Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
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.  ...  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  ...  Figure 4: G 1 Figure 5 : 5 G 2 2.3 Strong equality of hop domination and hop independent domination numbers In [6], Haynes et al. obtained strong equality of domination number and other domination parameters  ...

### Is observed direct CP violation in Bd→K+π− due to new physics? Check standard model prediction of equal violation in Bs→K−π+

Harry J. Lipkin
2005 Physics Letters B
A robust test of the standard model vs. new physics is its prediction of equal direct CP violation in B_s → K^- π^+ decay.  ...  But in the standard model a miracle occurs and the interfering tree diagram is enhanced by the same CKM factor that reduces the penguin to give the predicted equality.  ...  ACKNOWLEDGEMENTS This research was supported in part by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38.  ...

### On the total and strong version for Roman dominating functions in graphs [article]

S. Nazari-Moghaddam, M. Soroudi, S.M. Sheikholeslami, I.G. Yero
2019 arXiv   pre-print
For instance, we establish upper bounds for such parameter, and relate it with several parameters related to vertex domination in graphs, from which we remark the standard domination number, the total  ...  The total version of one strong Roman dominating function includes the additional property concerning the not existence of vertices of degree zero in the subgraph of G, induced by the set of vertices labeled  ...  Trees In this section, we present two bounds for the total strong Roman domination number of trees.  ...

### Construction of trees and graphs with equal domination parameters

Michael Dorfling, Wayne Goddard, Michael A. Henning, C.M. Mynhardt
2006 Discrete Mathematics
We provide a simple constructive characterization for trees with equal domination and independent domination numbers, and for trees with equal domination and total domination numbers.  ...  We also consider a general framework for constructive characterizations for other equality problems.  ...  [10] provided a constructive characterization of those trees with strong equality: that is, where every -set is an i-set.  ...

### Page 857 of The Journal of Applied Ecology Vol. 46, Issue 4 [page]

2009 The Journal of Applied Ecology
Among WbV S.D.elevation had a strong negative effect in Swaziland but a strong positive effect in Linyanti.  ...  Trees equal in height or taller than the surrounding vegetation were preferred, with no difference in response to these two categories (G = 1-9, d.f. = I, P > 0-1).  ...

### Inverse and Disjoint Connected Cototal Domination number of the Jump Graph of a Graph

Annie Jasmine S.E., K. Ameenal Bibi
2019 International Journal of Research in Advent Technology
Exact values of some standard graphs, bounds and the relationship of this parameter with other graph theoretic graph parameters are evaluated.  ...  Keywords: Inverse Domination number of the jump graph of a graph, Inverse Connected Cototal Dominating set of a jump graph, Inverse Connected Cototal Domination number of a jump graph, Disjoint Connected  ...  , various domination parameters have been defined.  ...

### Patterns and drivers of plant functional group dominance across the Western Hemisphere: a macroecological re-assessment based on a massive botanical dataset

Kristine Engemann, Brody Sandel, Brian J. Enquist, Peter Møller Jørgensen, Nathan Kraft, Aaron Marcuse-Kubitza, Brian McGill, Naia Morueta-Holme, Robert K. Peet, Cyrille Violle, Susan Wiser, Jens-Christian Svenning
2015 Botanical journal of the Linnean Society
Seven plant functional groups were considered, describing major differences in structure and function: epiphytes; climbers; ferns; herbs; shrubs; coniferous trees; and angiosperm trees.  ...  Our results support the prediction that future climate change and anthropogenic pressures could shift geographical patterns in dominance of plant functional groups, with probable consequences for ecosystem  ...  the State of California.  ...

### Exploring Correlation between Stand Structural Indices and Parameters across Three Forest Types of the Southeastern Italian Alps

Edoardo Alterio, Alessio Cislaghi, Gian Battista Bischetti, Tommaso Sitzia
2021 Forests
Strong correlations have been found between the Shannon index and the Mingling index, between the Gini index and the Diameter differentiation index, and between size dominance indices.  ...  The analysis of correlation can guide their selection in research applications and forest management, avoiding redundancies and loss of time during data collection.  ...  When Ti is equal to 0, the reference tree and its neighbors have the equal diameter size.  ...