@article{Yang2026, 
author = {Yang Yang and Yanyan Song and Zhanjun Si and Yi Liu},
title = {Spectra of quasi-corona and multiple Q-complemented-vertex join graphs},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {10205-10225},
keywords = {Laplacian spectrum, cospectral graph, Kirchhoff index, spanning tree, graph energy},
url = {https://www.sciopen.com/article/10.3934/math.2026422},
doi = {10.3934/math.2026422},
abstract = {The Q-complemented graph of a graph    G, denoted by    C  T  (  G  ), was obtained by adding a new vertex for each edge    u  v  ∈  E  (  G  ), where this new vertex was adjacent to all vertices of    G except    u and    v. In this paper, we introduced two new graph constructions based on    C  T  (  G  ), namely, the quasi-corona Q-complemented-vertex join        G    1    ⊙      G    2   and the multiple Q-complemented-vertex join        G    1    ▽      G    2  . We determined the adjacency, Laplacian, and signless Laplacian spectra of these composite graphs. Using these spectral results, we constructed infinite families of    A-,    L-, and    Q-cospectral graphs. Moreover, we derived explicit formulas for several key invariants of the new graphs, including the number of spanning trees, the Kirchhoff index, the signless Laplacian energy-like invariant, and graph energy. Furthermore, numerical experiments were provided to illustrate the structural properties of the proposed graphs, suggesting that the multiple Q-complemented-vertex join construction may exhibit certain small-world-like characteristics.}
}