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

The first multiplicative Zagreb index [Formula: see text] of a graph [Formula: see text] is the product of the square of every vertex degree, while the second multiplicative Zagreb index [Formula: see text] is the product of the products of degrees of pairs of adjacent vertices. In this paper, we give sharp lower bound for [Formula: see text] and upper bound for [Formula: see text] of trees with given distance [Formula: see text]-domination number, and characterize those trees attaining the bounds.

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

Discrete Applied Mathematics ◽

10.1016/j.dam.2017.04.032 ◽

2017 ◽

Vol 229 ◽

pp. 113-120 ◽

Cited By ~ 3

Author(s):

Lianying Miao ◽

Shiyou Pang ◽

Fang Liu ◽

Eryan Wang ◽

Xiaoqing Guo

Keyword(s):

Domination Number ◽

Extremal Values ◽

Eccentric Distance

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On extremal multiplicative Zagreb indices of trees with given domination number

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.03.058 ◽

2018 ◽

Vol 332 ◽

pp. 338-350 ◽

Cited By ~ 7

Author(s):

Shaohui Wang ◽

Chunxiang Wang ◽

Jia-Bao Liu

Keyword(s):

Domination Number ◽

Zagreb Indices

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Some Indices over a New Algebraic Graph

Journal of Mathematics ◽

10.1155/2021/5510384 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Nurten Urlu Özalan

Keyword(s):

Chromatic Number ◽

Spectral Properties ◽

Degree Sequence ◽

Domination Number ◽

Clique Number ◽

Zagreb Indices ◽

Irregularity Index ◽

Minimum Degrees

In this paper, we first introduce a new graph Γ N over an extension N of semigroups and after that we study and characterize the spectral properties such as the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index, and also perfectness for Γ N . Moreover, we state and prove some important known Zagreb indices on this new graph.

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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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