Abstract
Let \(G =(V_{G}, E_{G})\) be a simple connected graph with its vertex set \(V_{G}\) and edge set \(E_{G}\). The Mostar index Mo(G) was defined as \(Mo(G)=\sum \limits _{e=uv\in E(G)}|n_{u}-n_{v}|\), where \(n_{u}\) (resp., \(n_{v}\)) is the number of vertices whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u). In this study, we determine the first three minimum Mostar indices of tree-like phenylenes and characterize all the tree-like phenylenes attaining these values. At last, we give some numerical examples and discussion.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No.11971180), the Guangdong Provincial Natural Science Foundation (Grant No. 2019A1515012052), the Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4423, 2020JJ5612) and the Department of Education of Hunan Province (Grant No. 19A318).
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Liu, H., You, L., Chen, H. et al. On the first three minimum Mostar indices of tree-like phenylenes. J. Appl. Math. Comput. 68, 3615–3629 (2022). https://doi.org/10.1007/s12190-021-01677-9
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DOI: https://doi.org/10.1007/s12190-021-01677-9