2022

DOI: 10.1142/s0218348x2250181x

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The Hyper-Wiener Indices of Vicsek Networks

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Abstract: The hyper-Wiener index is an important topological invariant, which is based on the distance between two vertexes on a graph. This paper is concerned with the hyper-Wiener indices of Vicsek networks. Based on the method of finite pattern, we calculate the asymptotic formula of the hyper-Wiener indices of Vicsek networks.

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Cited by 4 publications

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Some Zagreb-Type Indices of Vicsek Polygon Graphs

WU,

XUE,

HE

et al. 2024

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Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs.

Some Zagreb-Type Indices of Vicsek Polygon Graphs

WU,

XUE,

HE

et al. 2024

View full text Add to dashboard Cite

Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs.

Edge-Wiener Index of Level-3 Sierpinski Skeleton Network

DU,

YAO,

XI

2024

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The edge-Wiener index is an important topological index in Chemical Graph Theory, defined as the sum of distances among all pairs of edges. Fractal structures have received much attention from scientists because of their philosophical and aesthetic significance, and chemists have even attempted to synthesize various types of molecular fractal structures. The level-3 Sierpinski triangle is constructed similarly to the Sierpinski triangle and its skeleton networks have self-similarity. In this paper, by using the method of finite pattern, we obtain the edge-Wiener index of skeleton networks according to level-3 Sierpinski triangle. This provides insights for a better understanding of molecular fractal structures.

Resistance Distances of Stretched Sierpinski Networks

FAN,

LI

2024

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