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Bounds on the strong domination number

2000
*
Discrete Mathematics
*

Whereas for

doi:10.1016/s0012-365x(99)00248-4
fatcat:rbnngfd7mjfp7gyphrrhaldjma
*the**strong**domination**number*there are many structural restrictions*on**the*graph (see [2] and [5] ) which affect this parameter, similar assumptions have no effect*on**the*weak*domination*... Preliminary Results In [6]*the*authors also introduced a*strong**domination**number*rst( G) which differs from 'Yw( G) only by*the*opposite degree demand. ...##
###
THE STRONG (WEAK) VV-DOMINATING SET OF A GRAPH

2019
*
Malaysian Journal of Science
*

*The*

*strong*vv-

*domination*

*number*γ ( ) is

*the*order of

*the*minimum

*strong*vv-

*dominating*set of G. Similarly weak vvdomination

*number*γ ( ) is defined. ... A set of vertices is said to be

*strong*vv-

*dominating*set if each vertex outside

*the*set is strongly vv-

*dominated*by at least

*one*vertex inside

*the*set. ... Several

*bounds*for

*strong*block

*domination*parameters are obtained. ...

##
###
Bounds on weak and strong total domination in graphs

2016
*
Electronic Journal of Graph Theory and Applications
*

*The*

*strong*total

*domination*

*number*γ st (G) of G is

*the*minimum cardinality of a

*strong*total

*dominating*set of G. We present some

*bounds*

*on*weak and

*strong*total

*domination*

*number*of a graph. ...

*The*weak total

*domination*

*number*γ wt (G) of G is

*the*minimum cardinality of a weak total

*dominating*set of G. ... Similarly we obtain

*the*following. Sharp

*bounds*

*on*

*the*

*strong*total

*domination*

*number*in trees Chellali et al. ...

##
###
On the global offensive alliance number of a graph

2009
*
Discrete Applied Mathematics
*

In this paper we obtain several tight

doi:10.1016/j.dam.2008.02.007
fatcat:nxb3gzs4h5gu5ha6ksldnm4gei
*bounds**on*γ o (Γ ) and γ co (Γ ) in terms of several parameters of Γ .*The*case of*strong*alliances is studied by analogy. ... In*the*case of*strong*offensive alliance, strict majority is required. An alliance S is called global if it affects every vertex in V \ S, that is, S is a*dominating*set of Γ . ... Notice that*the**bound*γ (Γ )+n 2*on*γ o (Γ ) is never worse than*the**bound*n+α(Γ ) 2 .*The*advantage of*the*second*one*is when there is known*the*independence*number*but not*the**domination**number*. ...##
###
On the global offensive alliance number of a graph
[article]

2006
*
arXiv
*
pre-print

*The*offensive alliance

*number*a_o(Γ) (respectively,

*strong*offensive alliance

*number*a_ô(Γ)) is

*the*minimum cardinality of an offensive (respectively,

*strong*offensive) alliance in Γ. ... In this paper we obtain several tight

*bounds*

*on*γ_o(Γ) and γ_ô(Γ) in terms of several parameters of Γ. ...

*The*study of offensive alliances was initiated by Favaron et al. in [2] where were derived several

*bounds*

*on*

*the*offensive alliance

*number*and

*the*

*strong*offensive alliance

*number*. ...

##
###
Strong Transversals in Hypergraphs and Double Total Domination in Graphs

2010
*
SIAM Journal on Discrete Mathematics
*

*The*set T is a

*strong*transversal in H if T contains at least two vertices from every edge of H.

*The*

*strong*transversal

*number*τ s (H) of H is

*the*minimum size of a

*strong*transversal in H. ...

*The*minimum cardinality of a double total

*dominating*set of G is

*the*double total

*domination*

*number*γ ×2,t (G) of G. Let G be a connected graph of order n with minimum degree at least three. ...

*The*set T is a

*strong*transversal in H if T contains at least two vertices from every edge of H.

*The*

*strong*transversal

*number*τ s (H) of H is

*the*minimum size of a

*strong*transversal in H. ...

##
###
Probabilistic Bounds On Weak And Strong Total Domination In Graphs

2016
*
Zenodo
*

A set D of vertices in a graph G = (V,E) is a total

doi:10.5281/zenodo.815745
fatcat:bblmcspxcjenflzayfffwb4frm
*dominating*set if every vertex of G is adjacent to some vertex in D. ... We obtain probabilistic upper*bounds**on*weak and*strong*total*domination**number*of a graph. §2. Results We adopt*the*notations of [1] . ...*The**strong*total*domination**number*γ st (G) of G is*the*minimum cardinality of a*strong*total*dominating*set of G. ...##
###
On fuzzy dominator coloring in fuzzy graphs

2015
*
Applied Mathematical Sciences
*

It is proved that fuzzy

doi:10.12988/ams.2015.4121015
fatcat:ddgihlowj5fstdqpeeaqudeofy
*dominator*chromatic*number*equals fuzzy chromatic*number*if at least*one*node of G has*strong*degree n-1. ...*Bounds*for fuzzy*dominator*chromatic*number*and necessary and sufficient condition for fuzzy*dominator*chromatic*number*to be 2 and n has been found. ... Then adding*the*edge u1un will preserve*the*FDC of Pn in Cn.*Bounds*of Fuzzy*Dominator*Chromatic*number*Let G be a connected fuzzy graph where*the**number*of nodes is n2. ...##
###
The inverse strong non-split r-domination number of a graph

2010
*
International Journal of Engineering, Science and Technology
*

We characterize graphs for which γ sns r(G) + γ′ sns r(G) = n, where γ sns r(G) is

doi:10.4314/ijest.v2i1.59102
fatcat:fq7562dafbd2df52j5r6sif4tq
*the**strong*non-split r-*domination**number*of G. We get many*bounds**on*γ′ sns r(G). ... In this paper, we define*the*notions of inverse*strong*non-split r-*dominating*set and inverse*strong*non-split r-*domination**number*γ′ sns r(G) of a graph G. ... Then r-clique is denoted by r ω (G) and is defined by*the*maximum order of r-complete vertices.*Bounds**on*γ sns ′r(G) Here, we get*bounds**on*γ sns ′r(G) through*the*following theorems. ...##
###
Strong Geodetic Domination of Graphs

2019
*
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
*

Here

doi:10.35940/ijitee.l2503.1081219
fatcat:rdy3jjv72remhlgpjgjybtxixa
*the**domination*concept is combined with*strong*geodetic concept resulting in*Strong*geodetic*domination*of graphs and few results are derived. ...*The*problem to find a where all points of*the*graph are covered by a unique fixed geodesic between*the*pair of points in is called*the**strong*geodetic problem. ... For , where*the*GD*number*is 2, while*the*SGD*number*is equal to -. Thus,*the*SGD*number*is not in*the*near*bound*of*the*GD*number*. ...##
###
On strong (weak) independent sets and vertex coverings of a graph

2007
*
Discrete Mathematics
*

*The*

*strong*(weak) vertex covering

*number*s = s (G) (w = w (G)) is

*the*minimum cardinality of an SVC (WVC). In this paper, we investigate some relationships among these four new parameters. ... Further, we show that s p − and w p − and find a necessary and sufficient condition to attain

*the*upper

*bound*, characterizing

*the*graphs which attain these

*bounds*. ... Acknowledgement

*The*authors are grateful to

*the*referees for their valuable comments and suggestions. ...

##
###
Page 65 of Mathematical Reviews Vol. , Issue 2001A
[page]

2001
*
Mathematical Reviews
*

*The*

*strong*

*domination*

*number*7,,(G) is defined as

*the*minimum cardinality of a

*strong*

*dominating*set and was introduced by E. Sampathkumar and L. ... Gaz. 49 (1965), 290-293; MR 32 #4025] that every n-vertex tournament is

*dominated*by at most lgn —Iglgn +2 vertices.” 2001a:05114 05C69 Rautenbach, Dieter (D-AACH-M2; Aachen)

*Bounds*

*on*

*the*

*strong*

*domination*...

##
###
BONDAGE AND NON-BONDAGE NUMBER OF A FUZZY GRAPH

2015
*
International Journal of Pure and Applied Mathematics
*

*The*bondage

*number*b(G) and non-bondage

*number*b n (G) of a fuzzy graph G are defined.

*The*upper

*bound*for both b(G) and b n (G) are given. Also some results

*on*b(G) and b n (G) are discussed. ...

*The*exact values of b(G) and b n (G) are determined for several classes of fuzzy graphs. ... In G, all arcs are

*strong*arcs. Thus

*the*total

*number*of (

*strong*) arcs in G are n(n − 1)/2. We know that γ(G) = 1. Each node will

*dominate*all other nodes. ...

##
###
Offensive alliances in cubic graphs

2006
*
International Mathematical Forum
*

In

doi:10.12988/imf.2006.06152
fatcat:6i4h3gvaxzhsnm6alhro76ydfi
*the*case of*strong*offensive alliance, strict majority is required. An alliance S is called Mathematics Subject Classification: 05C69; 15C05 ... An offensive alliance in a graph Γ = (V, E) is a set of vertices S ⊂ V where for every vertex v in its boundary it holds that*the*majority of vertices in v's closed neighborhood are in S. ...*The*particular case of global (*strong*) defensive alliance was investigated in [5] where several*bounds**on**the*global (*strong*) defensive alliance*number*were obtained. ...##
###
Inverse Independence Number of a Graph

2012
*
International Journal of Computer Applications
*

*The*inverse independence

*Number*β 0 -1 (G) = max { S : S is an inverse independent set of G}.We find few

*bounds*

*on*inverse

*domination*

*number*and also initiate

*the*study of

*the*inverse independence

*number*... giving few

*bounds*

*on*inverse independence

*number*of a graph. ...

*BOUNDS*

*ON*INVERSE

*DOMINATION*

*NUMBER*

*The*concept of inverse

*domination*is introduced by Kulli V.R and Sigarakanti S.C [9] . Let D be a -set of G. ...

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