The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number
The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G. In this paper, among the unicyclic graphs of order n, we p...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3589448 |
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| author | Luozhong Gong Weijun Liu |
| author_facet | Luozhong Gong Weijun Liu |
| author_sort | Luozhong Gong |
| collection | DOAJ |
| description | The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G. In this paper, among the unicyclic graphs of order n, we present the ordering of the unicyclic graphs with matching number 2 according to the λ1G values for n≥11 and also determine the graphs with the first and second largest λ1G values with matching number 3. |
| format | Article |
| id | doaj-art-fd78b4374e324f4bab961b6e2bdace0f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-fd78b4374e324f4bab961b6e2bdace0f2025-02-03T05:53:27ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3589448The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching NumberLuozhong Gong0Weijun Liu1School of MathematicsSchool of Mathematics and StatisticsThe matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as MGx=∑k=0n/2−1kmG,kxn−2k, where mG,k is the number of the k matchings of G. Let λ1G denote the largest matching root of the graph G. In this paper, among the unicyclic graphs of order n, we present the ordering of the unicyclic graphs with matching number 2 according to the λ1G values for n≥11 and also determine the graphs with the first and second largest λ1G values with matching number 3.http://dx.doi.org/10.1155/2022/3589448 |
| spellingShingle | Luozhong Gong Weijun Liu The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number Journal of Mathematics |
| title | The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number |
| title_full | The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number |
| title_fullStr | The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number |
| title_full_unstemmed | The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number |
| title_short | The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number |
| title_sort | ordering of the unicyclic graphs with respect to largest matching root with given matching number |
| url | http://dx.doi.org/10.1155/2022/3589448 |
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