| Summary: | The <i>complemented triangulation graph</i> of a graph <i>G</i>, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">CT</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula>, is defined as the graph obtained from <i>G</i> by adding, for each edge <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mi>v</mi></mrow></semantics></math></inline-formula> of <i>G</i>, a new vertex whose neighbours are the vertices of <i>G</i> other than <i>u</i> and <i>v</i>. In this paper, we first obtain the <i>A</i>-spectra, the <i>L</i>-spectra, and the <i>Q</i>-spectra of the complemented triangulation graphs of regular graphs. By using the results, we construct infinitely many pairs of <i>A</i>-cospectral graphs, <i>L</i>-cospectral graphs, and <i>Q</i>-cospectral graphs. We also obtain the number of spanning trees and the Kirchhoff index of the complemented triangulation graphs of regular graphs.
|
|---|