Domination in generalized Petersen graphs

Bohdan Zelinka

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 11-16
  • ISSN: 0011-4642

Abstract

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Generalized Petersen graphs are certain graphs consisting of one quadratic factor. For these graphs some numerical invariants concerning the domination are studied, namely the domatic number d ( G ) , the total domatic number d t ( G ) and the k -ply domatic number d k ( G ) for k = 2 and k = 3 . Some exact values and some inequalities are stated.

How to cite

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Zelinka, Bohdan. "Domination in generalized Petersen graphs." Czechoslovak Mathematical Journal 52.1 (2002): 11-16. <http://eudml.org/doc/30680>.

@article{Zelinka2002,
abstract = {Generalized Petersen graphs are certain graphs consisting of one quadratic factor. For these graphs some numerical invariants concerning the domination are studied, namely the domatic number $d(G)$, the total domatic number $d_t(G)$ and the $k$-ply domatic number $d^k(G)$ for $k=2$ and $k=3$. Some exact values and some inequalities are stated.},
author = {Zelinka, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {domatic number; total domatic number; $k$-ply domatic number; generalized Petersen graph; total domatic number; -ply domatic number; generalized Petersen graph},
language = {eng},
number = {1},
pages = {11-16},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Domination in generalized Petersen graphs},
url = {http://eudml.org/doc/30680},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Domination in generalized Petersen graphs
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 11
EP - 16
AB - Generalized Petersen graphs are certain graphs consisting of one quadratic factor. For these graphs some numerical invariants concerning the domination are studied, namely the domatic number $d(G)$, the total domatic number $d_t(G)$ and the $k$-ply domatic number $d^k(G)$ for $k=2$ and $k=3$. Some exact values and some inequalities are stated.
LA - eng
KW - domatic number; total domatic number; $k$-ply domatic number; generalized Petersen graph; total domatic number; -ply domatic number; generalized Petersen graph
UR - http://eudml.org/doc/30680
ER -

References

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  1. A note on the toughness of generalized Petersen graphs, J.  Math. Research & Exposition 12 (1987), 183–186. (1987) MR1167349
  2. 10.1002/net.3230070305, Networks 7 (1977), 247–261. (1977) MR0483788DOI10.1002/net.3230070305
  3. 10.1002/net.3230100304, Networks 10 (1980), 211–219. (1980) MR0584887DOI10.1002/net.3230100304
  4. On mapping graphs and permutation graphs, Math. Slovaca (1979), 215–228. (1979) 
  5. On the vulnerability of cycle permutation graphs, Ars Combinatoria 29 (1990), 289–296. (1990) MR1046114
  6. On k -ply domatic numbers of graphs, Math. Slovaca 34 (1985), 313–318. (1985) MR0756989

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