Abstract
The generalized Terminal Wiener Index is the sum of distances between each pair of vertices of degree k. In this paper, we proved the conjecture of reference [1]: when \({\text {k}}\ge 4\), the generalized terminal Wiener index of trees reaches its maximum value at \({\text {T}}_{{{\text {n}},{\text {k}},{\text {p}}}}\) caterpillars. We also determined the corresponding p value of the extremal graph.
The work is supported by training and plan projects of college students’ innovation and pioneering in grangdong province (No.1056413046).
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Acknowledgments
Support of the training and plan projects of college student’s innovation and pioneering in Guangzhou Province (No. 1056413046) is gratefully acknowledged. We are also grateful to the referees for their valuable comments and corrections, which lead to an improvement of the original manuscript.
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Chen, Df., Wei, Fy., Zhu, Hy., Wu, Y., Nong, Sz. (2016). Extremal Trees of Terminal Wiener Index. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_32
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DOI: https://doi.org/10.1007/978-3-319-19105-8_32
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