Analyzing lattice networks through substructures

Analyzing lattice networks through substructures Analyzing the topology of network structures is an important topic studied from many different aspects of science and mathematics. The Wiener polarity index (number of unordered pairs of vertices at distance 3 from each other) is one of the representative descriptors of graph structures. It was computed for several lattice networks by Chen et al. [11] in an effort to understand the properties of these networks. The Wiener polarity index is a variation of the classic distance-based graph invariant, the Wiener index (sum of distances between all pairs of vertices), which is known to be closely related to the number of substructures. In this paper we examine the numbers of various subgraphs of order 4 for these lattice networks. In addition to confirming their symmetric nature, comparing the numbers of various substructures leads to insights on other less trivial characteristics of these network structures of common interest. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Analyzing lattice networks through substructures

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.012
Publisher site
See Article on Publisher Site

Abstract

Analyzing the topology of network structures is an important topic studied from many different aspects of science and mathematics. The Wiener polarity index (number of unordered pairs of vertices at distance 3 from each other) is one of the representative descriptors of graph structures. It was computed for several lattice networks by Chen et al. [11] in an effort to understand the properties of these networks. The Wiener polarity index is a variation of the classic distance-based graph invariant, the Wiener index (sum of distances between all pairs of vertices), which is known to be closely related to the number of substructures. In this paper we examine the numbers of various subgraphs of order 4 for these lattice networks. In addition to confirming their symmetric nature, comparing the numbers of various substructures leads to insights on other less trivial characteristics of these network structures of common interest.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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