Decomposition of Cartesian product of complete graphs into paths and stars with four edges

Arockiajeyaraj P. Ezhilarasi; Appu Muthusamy

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 3, page 273-289
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Ezhilarasi, Arockiajeyaraj P., and Muthusamy, Appu. "Decomposition of Cartesian product of complete graphs into paths and stars with four edges." Commentationes Mathematicae Universitatis Carolinae 62.3 (2021): 273-289. <http://eudml.org/doc/297551>.

@article{Ezhilarasi2021,
abstract = {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 $\lbrace P_5,S_5\rbrace $-decomposition of Cartesian product of complete graphs.},
author = {Ezhilarasi, Arockiajeyaraj P., Muthusamy, Appu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {graph decomposition; path; star graph; product graph},
language = {eng},
number = {3},
pages = {273-289},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Decomposition of Cartesian product of complete graphs into paths and stars with four edges},
url = {http://eudml.org/doc/297551},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Ezhilarasi, Arockiajeyaraj P.
AU - Muthusamy, Appu
TI - Decomposition of Cartesian product of complete graphs into paths and stars with four edges
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 3
SP - 273
EP - 289
AB - 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 $\lbrace P_5,S_5\rbrace $-decomposition of Cartesian product of complete graphs.
LA - eng
KW - graph decomposition; path; star graph; product graph
UR - http://eudml.org/doc/297551
ER -

References

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  2. Abueida A. A., Daven M., Multidecompositions of the complete graph, Ars Combin. 72 (2004), 17–22. 
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  4. Abueida A. A., O'Neil T., Multidecomposition of λ K m into small cycles and claws, Bull. Inst. Combin. Appl. 49 (2007), 32–40. 
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  6. Ezhilarasi A. P., Muthusamy A., Decomposition of product graphs into paths and stars with three edges, Bull. Inst. Combin. Appl. 87 (2019), 47–74. 
  7. Jeevadoss S., Muthusamy A., 10.1007/s00373-015-1564-z, Graphs Combin. 32 (2016), 199–223. DOI10.1007/s00373-015-1564-z
  8. Priyadharsini H. M., Muthusamy A., ( G m , H m ) -multidecomposition of K m , m ( λ ) , Bull. Inst. Combin. Appl. 66 (2012), 42–48. 
  9. Shyu T.-W., Decomposition of complete graphs into paths and stars, Discrete Math. 310 (2010), no. 15–16, 2164–2169. 
  10. Shyu T.-W., 10.1016/j.disc.2012.12.020, Discrete Math. 313 (2013), no. 7, 865–871. DOI10.1016/j.disc.2012.12.020

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