Journal
DISCRETE APPLIED MATHEMATICS
Volume 254, Issue -, Pages 256-267Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.dam.2018.06.026
Keywords
Normalized Laplacian; Degree-Kirchhoff index; Spanning tree
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Funding
- National Natural Science Foundation of China [11601006, 11471016]
- Anhui Provincial Natural Science Foundation [KJ2015A331, KJ2013B105]
- Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities [CZY18032]
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Recently, Peng and Li (2017) derived an explicit closed formula of Kirchhoff index and the number of spanning trees of linear phenylenes and their dicyclobutadieno derivatives, respectively in terms of the Laplacian spectrum. At the same time, they pointed that it is natural and interesting to study the normalized Laplacian, degree-Kirchhoff index and counting the spanning tree numbers of linear phenylenes and their dicyclobutadieno derivatives, respectively. Motivated by these, in this paper, explicit closed-form formulas for degree-Kirchhoff index and the number of spanning trees of generalized phenylenes are obtained based on the normalized Laplacian spectrum, respectively. (C) 2018 Elsevier B.V. All rights reserved.
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