$G$-designs for the connected triangular bicyclic graphs with nine edges
A $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ exists whenever $n \equiv 0,1 \pmod{18}$.
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| Format: | Article |
| Language: | English |
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University of Isfahan
2024-11-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | https://toc.ui.ac.ir/article_28944_0251192f0ac271abed0c719b103dc4d4.pdf |
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| _version_ | 1846162383673753600 |
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| author | Bryan Freyberg Dalibor Froncek Joel Jeffries Gretta Jensen Andrew Sailstad |
| author_facet | Bryan Freyberg Dalibor Froncek Joel Jeffries Gretta Jensen Andrew Sailstad |
| author_sort | Bryan Freyberg |
| collection | DOAJ |
| description | A $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ exists whenever $n \equiv 0,1 \pmod{18}$. |
| format | Article |
| id | doaj-art-1fa22a1f7eaf44dc8aea9c34b8fa7269 |
| institution | Kabale University |
| issn | 2251-8657 2251-8665 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj-art-1fa22a1f7eaf44dc8aea9c34b8fa72692024-11-20T11:10:20ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652024-11-0114427128110.22108/toc.2024.140831.215628944$G$-designs for the connected triangular bicyclic graphs with nine edgesBryan Freyberg0Dalibor Froncek1Joel Jeffries2Gretta Jensen3Andrew Sailstad4Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MNDepartment of Mathematics and Statistics University of Minnesota Duluth 1117 University Dr. Duluth, MN 55812-3000 USADepartment of Mathematics, Iowa State University, 411 Morrill Road, Ames, USADepartment of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, USASchool of Mathematics, University of Minnesota, 127 Vincent Hall 206 Church St. SE, Minneapolis, USAA $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ exists whenever $n \equiv 0,1 \pmod{18}$.https://toc.ui.ac.ir/article_28944_0251192f0ac271abed0c719b103dc4d4.pdfgraph decompositionbicyclic graphsrho-labelings |
| spellingShingle | Bryan Freyberg Dalibor Froncek Joel Jeffries Gretta Jensen Andrew Sailstad $G$-designs for the connected triangular bicyclic graphs with nine edges Transactions on Combinatorics graph decomposition bicyclic graphs rho-labelings |
| title | $G$-designs for the connected triangular bicyclic graphs with nine edges |
| title_full | $G$-designs for the connected triangular bicyclic graphs with nine edges |
| title_fullStr | $G$-designs for the connected triangular bicyclic graphs with nine edges |
| title_full_unstemmed | $G$-designs for the connected triangular bicyclic graphs with nine edges |
| title_short | $G$-designs for the connected triangular bicyclic graphs with nine edges |
| title_sort | g designs for the connected triangular bicyclic graphs with nine edges |
| topic | graph decomposition bicyclic graphs rho-labelings |
| url | https://toc.ui.ac.ir/article_28944_0251192f0ac271abed0c719b103dc4d4.pdf |
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