The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two
The number of jj-matchings in a graph HH is denote by m(H,j)m\left(H,j). If for two graphs H1{H}_{1} and H2{H}_{2}, m(H1,j)≥m(H2,j)m\left({H}_{1},j)\ge m\left({H}_{2},j) for all jj, then we write H1≽H2{H}_{1}\succcurlyeq {H}_{2}. If H1≽H2{H}_{1}\succcurlyeq {H}_{2}, and m(H1,i)>m(H2,i)m\left({H}_...
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De Gruyter
2024-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0120 |
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| author | Bai Yongqiang Ma Hongping Zhang Xia |
| author_facet | Bai Yongqiang Ma Hongping Zhang Xia |
| author_sort | Bai Yongqiang |
| collection | DOAJ |
| description | The number of jj-matchings in a graph HH is denote by m(H,j)m\left(H,j). If for two graphs H1{H}_{1} and H2{H}_{2}, m(H1,j)≥m(H2,j)m\left({H}_{1},j)\ge m\left({H}_{2},j) for all jj, then we write H1≽H2{H}_{1}\succcurlyeq {H}_{2}. If H1≽H2{H}_{1}\succcurlyeq {H}_{2}, and m(H1,i)>m(H2,i)m\left({H}_{1},i)\gt m\left({H}_{2},i) for some ii, then we write H1≻H2{H}_{1}\hspace{0.33em}\succ \hspace{0.33em}{H}_{2}. In this article, by utilizing several new graph transformations, we determine the least element with respect to the quasi-order ≽\succcurlyeq among all unicyclic graphs with fixed order and number of vertices of degree two. As consequences, we characterize the graphs with minimum matching energy and with minimum Hosoya index in the set of all unicyclic graphs with fixed order and number of vertices of degree two. |
| format | Article |
| id | doaj-art-4732593a78e44776a25bdca8f77c9ac5 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-4732593a78e44776a25bdca8f77c9ac52025-01-07T07:55:58ZengDe GruyterOpen Mathematics2391-54552024-12-0122129332210.1515/math-2024-0120The minimum matching energy of unicyclic graphs with fixed number of vertices of degree twoBai Yongqiang0Ma Hongping1Zhang Xia2School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaThe number of jj-matchings in a graph HH is denote by m(H,j)m\left(H,j). If for two graphs H1{H}_{1} and H2{H}_{2}, m(H1,j)≥m(H2,j)m\left({H}_{1},j)\ge m\left({H}_{2},j) for all jj, then we write H1≽H2{H}_{1}\succcurlyeq {H}_{2}. If H1≽H2{H}_{1}\succcurlyeq {H}_{2}, and m(H1,i)>m(H2,i)m\left({H}_{1},i)\gt m\left({H}_{2},i) for some ii, then we write H1≻H2{H}_{1}\hspace{0.33em}\succ \hspace{0.33em}{H}_{2}. In this article, by utilizing several new graph transformations, we determine the least element with respect to the quasi-order ≽\succcurlyeq among all unicyclic graphs with fixed order and number of vertices of degree two. As consequences, we characterize the graphs with minimum matching energy and with minimum Hosoya index in the set of all unicyclic graphs with fixed order and number of vertices of degree two.https://doi.org/10.1515/math-2024-0120matching energyunicyclic graphquasi-orderhosoya index05c0905c92 |
| spellingShingle | Bai Yongqiang Ma Hongping Zhang Xia The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two Open Mathematics matching energy unicyclic graph quasi-order hosoya index 05c09 05c92 |
| title | The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| title_full | The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| title_fullStr | The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| title_full_unstemmed | The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| title_short | The minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| title_sort | minimum matching energy of unicyclic graphs with fixed number of vertices of degree two |
| topic | matching energy unicyclic graph quasi-order hosoya index 05c09 05c92 |
| url | https://doi.org/10.1515/math-2024-0120 |
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