| Title:
|
Decomposition of Cartesian product of complete graphs into paths and stars with four edges (English) |
| Author:
|
Ezhilarasi, Arockiajeyaraj P. |
| Author:
|
Muthusamy, Appu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
273-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $P_k$ and $S_k$ denote a path and a star, respectively, on $k$ vertices. We give necessary and sufficient conditions for the existence of a complete $\{P_5,S_5\}$-decomposition of Cartesian product of complete graphs. (English) |
| Keyword:
|
graph decomposition |
| Keyword:
|
path |
| Keyword:
|
star graph |
| Keyword:
|
product graph |
| MSC:
|
05C51 |
| MSC:
|
05C70 |
| idMR:
|
MR4331282 |
| DOI:
|
10.14712/1213-7243.2021.024 |
| . |
| Date available:
|
2021-10-18T08:28:46Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149144 |
| . |
| Reference:
|
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| Reference:
|
[2] Abueida A. A., Daven M.: Multidecompositions of the complete graph.Ars Combin. 72 (2004), 17–22. |
| Reference:
|
[3] Abueida A. A., Daven M., Roblee K. J.: Multidesigns of the $\lambda$-fold complete graph for graph-pairs of orders 4 and 5.Australas. J. Combin. 32 (2005), 125–136. |
| Reference:
|
[4] Abueida A. A., O'Neil T.: Multidecomposition of $\lambda K_m$ into small cycles and claws.Bull. Inst. Combin. Appl. 49 (2007), 32–40. |
| Reference:
|
[5] Bondy J. A., Murty U. S. R.: Graph Theory with Applications.American Elsevier Publishing, New York, 1976. |
| Reference:
|
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| Reference:
|
[7] Jeevadoss S., Muthusamy A.: Decomposition of product graphs into paths and cycles of length four.Graphs Combin. 32 (2016), 199–223. 10.1007/s00373-015-1564-z |
| Reference:
|
[8] Priyadharsini H. M., Muthusamy A.: $(G_m, H_m)$-multidecomposition of $K_{m,m}(\lambda)$.Bull. Inst. Combin. Appl. 66 (2012), 42–48. |
| Reference:
|
[9] Shyu T.-W.: Decomposition of complete graphs into paths and stars.Discrete Math. 310 (2010), no. 15–16, 2164–2169. |
| Reference:
|
[10] Shyu T.-W.: Decomposition of complete bipartite graphs into paths and stars with same number of edges.Discrete Math. 313 (2013), no. 7, 865–871. 10.1016/j.disc.2012.12.020 |
| . |
