Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix

Dehmer, Matthias; Marcel, Moosbrugger,; Shi, Yongtang

doi:10.1016/j.amc.2015.04.115

Cited by 12 publications

(4 citation statements)

References 22 publications

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“…It is worth mentioning that many numerical results and analyses have been obtained, which we refer the details to [17,23,27,28,33,42,55,56]. These numerical results imply that the change of different entropies corresponds to different structural properties of graphs.…”

Section: Discussionmentioning

confidence: 88%

A survey of recent results in (generalized) graph entropies

Li¹,

Wei²

2015

Preprint

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The entropy of a graph was first introduced by Rashevsky [1] and Trucco [2] to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of definitions of graph entropy measures and generalized graph entropies. Then we survey the known results about them from the following three respects: inequalities and extremal properties on graph entropies, relationships between graph structures, graph energies, topological indices and generalized graph entropies, complexity for calculation of graph entropies. Various applications of graph entropies together with some open problems and conjectures are also presented for further research.

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Section: Discussionmentioning

confidence: 88%

A survey of recent results in (generalized) graph entropies

Li¹,

Wei²

2015

Preprint

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“…Here, we argue that these zeros can serve as measures of the structural complexity of a directed graph. These measures are similar to those defined as a function of the eigenvalues of certain graph polynomials, see, e.g., [24, 25]. The eigenvalue based measures, represented by Eqs (33)–(36), have been defined with an eye to reducing their degeneracy, see also [24–26].…”

Section: Methodsmentioning

confidence: 99%

Measuring the complexity of directed graphs: A polynomial-based approach

et al. 2019

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In this paper, we define novel graph measures for directed networks. The measures are based on graph polynomials utilizing the out- and in-degrees of directed graphs. Based on these polynomial, we define another polynomial and use their positive zeros as graph measures. The measures have meaningful properties that we investigate based on analytical and numerical results. As the computational complexity to compute the measures is polynomial, our approach is efficient and can be applied to large networks. We emphasize that our approach clearly complements the literature in this field as, to the best of our knowledge, existing complexity measures for directed graphs have never been applied on a large scale.

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“…For more results on this topic, readers may refer to [14]. As the research developed, some researchers tried to use some kind of topological index or a few topological indices for classification based on isomorphism [3][4][5]. The main problem of classification based on isomorphism is that the topological indices may be identical even for two or several non-isomorphic graphs and the situation becomes worse with the increment of vertices of graph [6].…”

Section: Introductionmentioning

confidence: 99%

A Relation on Trees and the Topological Indices Based on Subgraph

Song¹,

Huang²

2022

MATCH

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A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to characterize non-isomorphic graphs with the same topological index value. By introducing a relation on trees with respect to edge division vectors, denoted by T n , , in this paper we give some results for the relation order in T n , , it allows us to compare the size of the topological index value without relying on the specific forms of them, and naturally we can determine which trees have the same topological index value. Based on these results we characterize some classes of trees that are uniquely determined by their edge division vectors and construct infinite classes of non-isomorphic trees with the same topological index value, particularly such trees of order no more than 10 are completely determined.

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Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix

Cited by 12 publications

References 22 publications

A survey of recent results in (generalized) graph entropies

A survey of recent results in (generalized) graph entropies

Measuring the complexity of directed graphs: A polynomial-based approach

A Relation on Trees and the Topological Indices Based on Subgraph

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