On the extremal values of the eccentric distance sum of trees with a given domination number

2020 ◽

Vol 12 (04) ◽

pp. 2050052 ◽

Cited By ~ 1

Author(s):

Lidan Pei ◽

Xiangfeng Pan

Keyword(s):

Positive Integer ◽

Connected Graph ◽

Dominating Set ◽

Domination Number ◽

Dominating Sets ◽

Minimum Cardinality ◽

Number Formula ◽

Simple Connected Graph ◽

Eccentric Distance ◽

Distance Formula

Let [Formula: see text] be a positive integer and [Formula: see text] be a simple connected graph. The eccentric distance sum of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the maximum distance from [Formula: see text] to any other vertex and [Formula: see text] is the sum of all distances from [Formula: see text]. A set [Formula: see text] is a distance [Formula: see text]-dominating set of [Formula: see text] if for every vertex [Formula: see text], [Formula: see text] for some vertex [Formula: see text]. The minimum cardinality among all distance [Formula: see text]-dominating sets of [Formula: see text] is called the distance [Formula: see text]-domination number [Formula: see text] of [Formula: see text]. In this paper, the trees among all [Formula: see text]-vertex trees with distance [Formula: see text]-domination number [Formula: see text] having the minimal eccentric distance sum are determined.

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Extremal values on Zagreb indices of trees with given distance k-domination number

Journal of Inequalities and Applications ◽

10.1186/s13660-017-1597-3 ◽

2018 ◽

Vol 2018 (1) ◽

Cited By ~ 4

Author(s):

Lidan Pei ◽

Xiangfeng Pan

Keyword(s):

Domination Number ◽

Zagreb Indices ◽

Extremal Values

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On the extremal values of the eccentric distance sum of trees

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.01.022 ◽

2012 ◽

Vol 390 (1) ◽

pp. 99-112 ◽

Cited By ~ 30

Author(s):

Shuchao Li ◽

Meng Zhang ◽

Guihai Yu ◽

Lihua Feng

Keyword(s):

Extremal Values ◽

Eccentric Distance

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On the extremal values of the eccentric distance sum of trees with a given maximum degree

Discrete Applied Mathematics ◽

10.1016/j.dam.2020.03.059 ◽

2020 ◽

Vol 284 ◽

pp. 375-383

Author(s):

Lianying Miao ◽

Jingru Pang ◽

Shoujun Xu

Keyword(s):

Maximum Degree ◽

Extremal Values ◽

Eccentric Distance

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The Domination Complexity and Related Extremal Values of Large 3D Torus

Complexity ◽

10.1155/2018/3041426 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Zehui Shao ◽

Jin Xu ◽

S. M. Sheikholeslami ◽

Shaohui Wang

Keyword(s):

Dominating Set ◽

Domination Number ◽

Molecular Graph ◽

Structural Complexity ◽

Minimum Size ◽

Molecular Graphs ◽

Computer Aided ◽

Extremal Values

Domination is a structural complexity of chemical molecular graphs. A dominating set in a (molecular) graphG=V,Eis a subsetS⊆Vsuch that each vertex inV\Sis adjacent to at least one vertex inS. The domination numberγGof a graphGis the minimum size of a dominating set inG. In this paper, computer-aided approaches for obtaining bounds for domination number on torus graphs are here considered, and many new exact values and bounds are obtained.

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Extremal values on the eccentric distance sum of trees

Discrete Applied Mathematics ◽

10.1016/j.dam.2013.05.023 ◽

2013 ◽

Vol 161 (16-17) ◽

pp. 2427-2439 ◽

Cited By ~ 32

Author(s):

Xianya Geng ◽

Shuchao Li ◽

Meng Zhang

Keyword(s):

Extremal Values ◽

Eccentric Distance

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Sharp lower bounds on the sum-connectivity index of trees

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830921501536 ◽

2021 ◽

Author(s):

S. Alyar ◽

R. Khoeilar

Keyword(s):

Lower Bounds ◽

Domination Number ◽

Extremal Problems ◽

Connectivity Index ◽

Matching Number ◽

Extremal Graphs ◽

Extremal Values

The sum-connectivity index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. In this paper, some extremal problems on the sum-connectivity index of trees are studied. The extremal values on the sum-connectivity index of trees with given graphic parameters, such as pendant number, matching number, domination number and diameter, are determined. The corresponding extremal graphs are characterized, respectively.

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