Spectra of Complemented Triangulation Graphs
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><...
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/17/3168 |
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| author | Jia Wei Jing Wang |
| author_facet | Jia Wei Jing Wang |
| author_sort | Jia Wei |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T01:32:45Z |
| format | Article |
| id | doaj.art-9682a4a9911a41bd8475d3cead8f5704 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:32:45Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-9682a4a9911a41bd8475d3cead8f57042023-11-23T13:39:38ZengMDPI AGMathematics2227-73902022-09-011017316810.3390/math10173168Spectra of Complemented Triangulation GraphsJia Wei0Jing Wang1School of Education, Lanzhou University of Arts and Science, Lanzhou 730000, ChinaSchool of Education, Lanzhou University of Arts and Science, Lanzhou 730000, ChinaThe <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.https://www.mdpi.com/2227-7390/10/17/3168<i>A</i>-spectrum<i>L</i>-spectrum<i>Q</i>-spectrumcomplemented triangulation graph |
| spellingShingle | Jia Wei Jing Wang Spectra of Complemented Triangulation Graphs Mathematics <i>A</i>-spectrum <i>L</i>-spectrum <i>Q</i>-spectrum complemented triangulation graph |
| title | Spectra of Complemented Triangulation Graphs |
| title_full | Spectra of Complemented Triangulation Graphs |
| title_fullStr | Spectra of Complemented Triangulation Graphs |
| title_full_unstemmed | Spectra of Complemented Triangulation Graphs |
| title_short | Spectra of Complemented Triangulation Graphs |
| title_sort | spectra of complemented triangulation graphs |
| topic | <i>A</i>-spectrum <i>L</i>-spectrum <i>Q</i>-spectrum complemented triangulation graph |
| url | https://www.mdpi.com/2227-7390/10/17/3168 |
| work_keys_str_mv | AT jiawei spectraofcomplementedtriangulationgraphs AT jingwang spectraofcomplementedtriangulationgraphs |