Resistance Distance-Based Indices and Spanning Trees of Linear Pentagonal-Quadrilateral Networks

Abstract

Let Q_n be the linear pentagonal-quadrilateral chain containing 2n pentagons and n squares. In this paper, we determined the (normalized) Laplacian spectra of Q_n based on the decomposition techniques for the corresponding matrices. Further, we obtained explicit expressions for (multiplicative degree-) Kirchhoff index and the number of spanning trees of linear pentagonal-quadrilateral chains which are based on relationships between the coefficients and roots.

Keywords:

• Laplacian matrix
• Kirchhoff
• index
• normalized
• Laplacian matrix
• spanning tree
• multiplicative degree-Kirchhoff index

Acknowledgment

The authors would like to express their sincere gratitude to the anonymous referees for valuable suggestions, which led to a great deal of improvement in the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially supported by University Natural Science Research Project of Anhui Province (No. KJ2020A0001) and Natural Science Foundation of Anhui Province (No. 2108085MA02).