On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges
A tree containing exactly two non-pendant vertices is called a double-star. Let k1 and k2 be two positive integers. The double-star with degree sequence (k1+1, k2+1, 1, ..., 1) is denoted by Sk1, k2. It is known that a cubic graph has an S1,1-decomposition if and only if it contains...
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| Format: | Article |
| Language: | English |
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University of Kashan
2018-06-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_63511_00671cbdab52608c7230f8055860c91a.pdf |
| _version_ | 1797630913303019520 |
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| author | Abbas Seify |
| author_facet | Abbas Seify |
| author_sort | Abbas Seify |
| collection | DOAJ |
| description | A tree containing exactly two non-pendant vertices is called a double-star. Let k1 and k2 be two positive integers. The double-star with degree sequence (k1+1, k2+1, 1, ..., 1) is denoted by Sk1, k2. It is known that a cubic graph has an S1,1-decomposition if and only if it contains a perfect matching. In this paper, we study the S1,2-decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an S1,2-decomposition in cubic graphs. |
| first_indexed | 2024-03-11T11:13:37Z |
| format | Article |
| id | doaj.art-88f8e316b46d4ac2aff61d6975bd711c |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:37Z |
| publishDate | 2018-06-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-88f8e316b46d4ac2aff61d6975bd711c2023-11-11T08:09:51ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652018-06-0131677410.22052/mir.2018.115910.108763511On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four EdgesAbbas Seify0Department of Sciences, Shahid Rajaei Teacher Training University, Tehran, I. R. IranA tree containing exactly two non-pendant vertices is called a double-star. Let k1 and k2 be two positive integers. The double-star with degree sequence (k1+1, k2+1, 1, ..., 1) is denoted by Sk1, k2. It is known that a cubic graph has an S1,1-decomposition if and only if it contains a perfect matching. In this paper, we study the S1,2-decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an S1,2-decomposition in cubic graphs.https://mir.kashanu.ac.ir/article_63511_00671cbdab52608c7230f8055860c91a.pdfedge-decompositiondouble-starcubic graphregular graphbipartite graph |
| spellingShingle | Abbas Seify On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges Mathematics Interdisciplinary Research edge-decomposition double-star cubic graph regular graph bipartite graph |
| title | On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges |
| title_full | On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges |
| title_fullStr | On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges |
| title_full_unstemmed | On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges |
| title_short | On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges |
| title_sort | on edge decomposition of cubic graphs into copies of the double star with four edges |
| topic | edge-decomposition double-star cubic graph regular graph bipartite graph |
| url | https://mir.kashanu.ac.ir/article_63511_00671cbdab52608c7230f8055860c91a.pdf |
| work_keys_str_mv | AT abbasseify onedgedecompositionofcubicgraphsintocopiesofthedoublestarwithfouredges |