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 uv 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.
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