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A graph is -excellent if every vertex of the graph is contained in some minimum dominating set of the graph. A vertex v is critical in G if the domination number of G − v is smaller than that of G. ... In this paper we show that these three properties, along with several others, are equivalent for trees on at least four vertices. We also provide a constructive characterization of these trees. ... Clearly, every restrained dominating set for a graph G is also an end-dominating set. The next theorem is from Hattingh and Henning  . Theorem 3.1 (Hattingh and Henning  ). ...doi:10.1016/j.disc.2006.02.016 fatcat:k7hkttq6pvegremd6wn4nlqpie
A graph G = (V (G), E(G)) is γ-excellent if V (G) is the union of all γ-sets of G, where γ stands for the domination number of G and a γ-set is a dominating set of cardinality γ. ... We consider some well-known graphs, including cycles, trees and some cartesian products of two graphs, and for every considered graph we describe its largest set H I for which the graph is H-γ-excellent ... The minimum cardinality of a set S which is simultaneously total dominating and restrained dominating in G is called the total restrained domination number γ tr (G) of G. ...doi:10.47443/dml.2020.0052 fatcat:apo7zz5dlbg7xidkhzkloqzgga
A graph G=(V,E) is γ-excellent if V is a union of all γ-sets of G, where γ stands for the domination number. Let ℐ be a set of all mutually nonisomorphic graphs and ∅≠ℋ⊊ℐ. ... For each of some well known graphs, including cycles, trees and some cartesian products of two graphs, we describe its largest set ℋ⊊ℐ for which the graph is ℋ-γ-excellent. ... The minimum cardinality of a set S which is simultaneously total dominating and restrained dominating in G is called the total restrained domination number γ tr (G) of G. ...arXiv:2010.03219v1 fatcat:qdopeiq6gveybf2b3nkjed2pfy
Lastly, we constructively characterize the trees T in which every vertex belongs to some weakly connected dominating set of cardinality wc (T ). ... We provide a constructive characterization of trees T for which (T ) = wc (T ). ... Characterizations of ( , )-trees include ( , i)-trees [1, 6] , trees with equal independent domination and restrained domination numbers, trees with equal independent domination and weak domination numbers ...doi:10.1016/j.disc.2005.10.006 fatcat:ozdpz7nugzc7th4tmvtkjue4ju
“Winter Shadows” is excellent in its blue-black tone, but it seems to lack a center of interest. H. J. ... “HIS COMPANIONS, INNOCENCE AND HEALTH, AND HIS BEST RICHES, IGNORANCE OF WEALTH > THIRD PRIZE — BEGINNERS CONTEST “The Cloud Over the Sun” is well named; it cer- tainly dominates the picture. ...
A Green Tree and a Dry Tree. CARTER WILSON. New York: Macmillan, 1972. 300 pp., maps, notes. $7.95 (cloth). Reviewed by GARY H. ... This observation in no way detracts from the re- viewer’s opinion as to the general excellence of this work. ...
American Journal of Theology
Spence’s proposals are so elaborate as to hinder their excellent purpose. ... In the rise of this principle as a dominating factor in our private life is the assurance of eventual reunion. ‘It must be evident to all,” says Dr. ...
In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic ... We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum ... The restrained domination number of G, denoted by γ r (G), is the minimum cardinality of a restrained dominating set of G. ...doi:10.1016/j.akcej.2016.06.007 fatcat:i7xnfbn2pbhozf6iltjbzi5try
The dominant party deter- mined to discipline his mind by confining his body. ... For now that God hath cut this tree of Para- dise down from its seat of earth, yet so the dead trunk may support x part of the declining temple, or, at least, serve to kindle the fire on the altar. ...
The ranking of the subjects was much the same for Restraining and Genital display. ... Restraining and Genital display showed quasi-linear hierarchies, with males on top and females at the bottom of them. ... In addition to the varied ways in which dominance could be achieved, it was also pointed out that the social functions of highly dominant animals were far richer than is implied by defining dominance in ...doi:10.1007/bf02382741 fatcat:2yv5mwvbrrdipejdspr65r3d6e
“The Cloud Over the Sun” is well named; it cer- tainly dominates the picture. ... Even then there would remain an excellent cloud- effect, occupying fully two-thirds of the picture-area, and the spacing of the whole composition would be improved. ...
Leymus chinensis was first divided into its own group and then separated into four groups via cluster tree analysis. ... All data were processed, and the graphs were plotted by Microsoft Excel 2010. ... Figure 3 . 3 Species cluster tree map of importance values. Figure 3 . 3 Species cluster tree map of importance values. ...doi:10.3390/su11102854 fatcat:hzerro7psncrhadxbcimqd3aby
We follow the concept of excellent tree and characterize the family of trees such that any vertex belongs to some independent [1, 2]-set. ... An [1, k]-set S in a graph G is a dominating set such that every vertex not in S has at most k neighbors in it. ... This concept has been studied in the family of trees for different domination-type properties such as domination, irredundance and independence [6, 9] , restrained domination  and total domination ...doi:10.7151/dmgt.2029 fatcat:j2mumtbqmjghhppslemzztfxbu
We follow the concept of excellent tree and characterize the family of trees such that any vertex belong to some independent [1,2]-set. ... An independent [1,k]-set S in a graph G is a dominating set which is independent and such that every vertex not in S has at most k neighbors in it. ... This concept has been studied in the family of trees for different domination-type properties such as domination, irredundance and independence [4, 7] , restrained domination  and total domination ...arXiv:1511.09262v1 fatcat:x5x6sxcfbbgjdhf4oqsquzbsgm
Eclectic Magazine of Foreign Literature
But if Rossetti has not magically in¬ terpreted external nature, if the literary instinct in him occasionally too marked¬ ly dominates the purely poetic, there is one point wherein he excels any contem ... urgent wood-notes soar, to turn to the unlabored and impulsive strain of the Scottish singer— The mavis sings fu blithely On ilka leafy bough ; or to the English poet’s— Hark \ where my blossomed pear-tree ...
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