Power domination in certain chemical structures

Stephen, Sudeep; Rajan, Bharati; Ryan, Joe; Grigorious, Cyriac; William, Albert

doi:10.1016/j.jda.2014.12.003

Cited by 14 publications

(10 citation statements)

References 15 publications

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“…A well known power domination subgraph relation is introduced by Sudeep Stephen in [15], which is stated as Theorem 2.1: (Power domination-subgraph relation). Let K 1 , .…”

Section: Preliminary Resultsmentioning

confidence: 99%

Domination and Power Domination in Certain Families of Nanostars Dendrimers

2020

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Dendrimers are hyper-branched macromolecules having various applications in diverse fields like supra-molecular chemistry, drug delivery and nanotechnology etc. The certain graph invariants such as dominating number and power dominating number can be used to characterize large number of physical properties like physio-chemical properties, thermodynamic properties, chemical and biological activities, etc. A subset of a simple undirected graph is called dominating set if every vertex of the given graph is either in that set or is adjacent to some vertex in that set. The minimum number of elements in that kind of set is called domination number. A subset of the vertex set of a graph G is said to be power dominating set (PDS) of G, if every vertex and every edge in G is observed by P. The minimum cardinality of P of a graph G is called power domination number. In this paper, the domination number and power domination number of some nanostars dendrimers have been determined.

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“…A well known power domination subgraph relation is introduced by Sudeep Stephen in [15], which is stated as Theorem 2.1: (Power domination-subgraph relation). Let K 1 , .…”

Section: Preliminary Resultsmentioning

confidence: 99%

Domination and Power Domination in Certain Families of Nanostars Dendrimers

2020

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“…us, the set of all distinct degree sums S u for u ∈ V(SSL(n)) is 11,14,16,17,18,19,26,28,30 { }. From the above information and the construction of the graph, the edge partition is calculated as follows.…”

Section: Proofmentioning

confidence: 99%

“…We review the degree-based topological descriptors for the RO(p, q, r) rhenium trioxide lattice in this section. [28]. It consists of rhenium atoms and oxygen atoms and is an inorganic compound.…”

Section: Rhenium Trioxide Latticementioning

confidence: 99%

Degree-Based Indices of Some Complex Networks

Ding

Bokhary

Rehman

et al. 2021

Journal of Mathematics

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A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph. Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, and geometric-arithmetic index GA are of great importance in the QSAR/QSPR analysis and are used to estimate the networks. In this area of research, graph theory has been found of considerable use. In this paper, the distinct degrees and degree sums of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. Utilizing these edge partitions, the closed formulae for some degree-based topological indices of the networks are deduced.

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“…In 2005 Liao et al have obtained that the power domination number for split graphs, a subclass of chordal graphs, an NP-complete. The power domination problem was solved for block graphs [4], product graphs [5], cylinder, torus and generalized Petersen graphs [6], certain chemical structures [7], honeycomb network [3], hexagonal grid [8] and so on.…”

Section: Introductionmentioning

confidence: 99%