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Spectra of Complemented Triangulation Graphs

Author

Listed:
  • Jia Wei

    (School of Education, Lanzhou University of Arts and Science, Lanzhou 730000, China)

  • Jing Wang

    (School of Education, Lanzhou University of Arts and Science, Lanzhou 730000, China
    School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China)

Abstract

The complemented triangulation graph of a graph G , denoted by CT ( G ) , is defined as the graph obtained from G by adding, for each edge u v of G , a new vertex whose neighbours are the vertices of G other than u and v . In this paper, we first obtain the A -spectra, the L -spectra, and the Q -spectra of the complemented triangulation graphs of regular graphs. By using the results, we construct infinitely many pairs of A -cospectral graphs, L -cospectral graphs, and Q -cospectral graphs. We also obtain the number of spanning trees and the Kirchhoff index of the complemented triangulation graphs of regular graphs.

Suggested Citation

  • Jia Wei & Jing Wang, 2022. "Spectra of Complemented Triangulation Graphs," Mathematics, MDPI, vol. 10(17), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3168-:d:905597
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    References listed on IDEAS

    as
    1. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
    2. Fei Wen & You Zhang & Muchun Li, 2019. "Spectra of Subdivision Vertex-Edge Join of Three Graphs," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    3. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
    4. Jia-Bao Liu & Yan Bao & Wu-Ting Zheng & Sakander Hayat, 2021. "NETWORK COHERENCE ANALYSIS ON A FAMILY OF NESTED WEIGHTED n-POLYGON NETWORKS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-15, December.
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