Third Smallest Wiener Polarity Index of Unicyclic Graphs

In this paper, we propose a family of unicyclic graphs to study robustness of network coherence quantified by the Laplacian spectrum, which measures the extent of consensus under the noise. We adjust the network parameters to change the structural asymmetries with an aim of studying their effects on the coherence. Using the graph’s structures and matrix theories, we obtain closed-form solutions of the network coherence regarding network parameters and network size. We further show that the coherence of the asymmetric graph is higher than the corresponding symmetric graph and also compare the consensus behaviors for the graphs with different asymmetric structures. It displays that the coherence of the unicyclic graph with one hub is better than the graph with two hubs. Finally, we investigate the effect of degree of hub nodes on the coherence and find that bigger difference of degrees leads to better coherence.

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Robustness of network coherence in asymmetric unicyclic graphs

Chen

Jing

Sun

2021

Int. J. Mod. Phys. B

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Wiener Polarity Index Calculation of Square-Free Graphs and Its Implementation to Certain Complex Materials

Zhang

Sun

Arockiaraj³

et al. 2021

Mathematical Problems in Engineering

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Molecular topology is a portion of mathematical chemistry managing the logarithmic portrayal of chemical materials, permitting a tremendous yet straightforward characterization of the compounds. Concerning the traditional physical-chemical descriptors, it is conceivable to set up direct quantitative structure-activity relationship methods to associate with such descriptors termed topological indices. In this study, we have developed the mathematical technique to study the Wiener polarity index of chemical materials without squares. We have taken the cancer treatment drugs such as lenvatinib and cabozantinib to illustrate our approach. In addition, we explored the inherent property of silicate, Sierpiński, and octahedral-related complex materials that the edge set can be decomposed in such a way that any edge in the same part of the decomposition has an equal number of neighboring vertices and applied the technique to derive the formulae for these materials.

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Third Smallest Wiener Polarity Index of Unicyclic Graphs

Cited by 2 publications

References 7 publications

Robustness of network coherence in asymmetric unicyclic graphs

Robustness of network coherence in asymmetric unicyclic graphs

Wiener Polarity Index Calculation of Square-Free Graphs and Its Implementation to Certain Complex Materials

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