Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index

Su, Guifu; Tu, Jianhua; Das, Kinkar Ch.

doi:10.1016/j.amc.2015.08.060

Cited by 15 publications

(11 citation statements)

References 10 publications

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“…The first Zagreb index is a well-known vertex-degreebased molecular structure descriptor. This index was first time considered by Gutman and Trinajstic about 45 years ago, and since then discussed and used in numerous studies (see [38][39][40] and the references cited therein). The first Zagreb index is defined as (2) where du denotes the degree (=number of first neighbors) of the vertex u in graph G. If G is a simple graph (i.e.…”

Section: (25 + ) Dimensional Feature Vectormentioning

confidence: 99%

Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

Zhao

Wang

et al. 2018

CCHTS

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Aim and Objective: The rapid increase in the amount of protein sequence data available leads to an urgent need for novel computational algorithms to analyze and compare these sequences. This study is undertaken to develop an efficient computational approach for timely encoding protein sequences and extracting the hidden information. Methods: Based on two physicochemical properties of amino acids, a protein primary sequence was converted into a three-letter sequence, and then a graph without loops and multiple edges and its geometric line adjacency matrix were obtained. A generalized PseAAC (pseudo amino acid composition) model was thus constructed to characterize a protein sequence numerically. Results: By using the proposed mathematical descriptor of a protein sequence, similarity comparisons among β-globin proteins of 17 species and 72 spike proteins of coronaviruses were made, respectively. The resulting clusters agreed well with the established taxonomic groups. In addition, a generalized PseAAC based SVM (support vector machine) model was developed to identify DNA-binding proteins. Experiment results showed that our method performed better than DNAbinder, DNA-Prot, iDNA-Prot and enDNA-Prot by 3.29-10.44% in terms of ACC, 0.056-0.206 in terms of MCC, and 1.45-15.76% in terms of F1M. When the benchmark dataset was expanded with negative samples, the presented approach outperformed the four previous methods with improvement in the range of 2.49-19.12% in terms of ACC, 0.05-0.32 in terms of MCC, and 3.82-33.85% in terms of F1M. Conclusion: These results suggested that the generalized PseAAC model was very efficient for comparison and analysis of protein sequences, and very competitive in identifying DNA-binding proteins.

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Section: (25 + ) Dimensional Feature Vectormentioning

confidence: 99%

Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

Zhao

Wang

et al. 2018

CCHTS

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“…0 R α (G) is the inverse degree [28], the zeroth-Randić index [29], the first Zagreb index [30], and the forgotten index [31] when α = −1, α = − 1 2 , α = 2, and α = 3, respectively. For some recent results on the general zeroth-order Randić index, one can see [32][33][34].…”

Section: The General Zeroth-order Randić Index and K-partitenessmentioning

confidence: 99%

The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Gao

Zhou

et al. 2018

Mathematics

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The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

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“…Jamil et al [21] investigated the extremal graphs of k-generalized quasi trees for zeroth-order general Randić index. For further results we refer to [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Some Bounds on Zeroth-Order General Randić Index

et al. 2020

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For a graph G without isolated vertices, the inverse degree of a graph G is defined as I D ( G ) = ∑ u ∈ V ( G ) d ( u ) − 1 where d ( u ) is the number of vertices adjacent to the vertex u in G. By replacing − 1 by any non-zero real number we obtain zeroth-order general Randić index, i.e., 0 R γ ( G ) = ∑ u ∈ V ( G ) d ( u ) γ , where γ ∈ R − { 0 } . Xu et al. investigated some lower and upper bounds on I D for a connected graph G in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0 . The corresponding extremal graphs have also been identified.

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Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index

Cited by 15 publications

References 10 publications

Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Some Bounds on Zeroth-Order General Randić Index

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