The basis number of some special non-planar graphs
Salar Y. Alsardary; Ali A. Ali
Czechoslovak Mathematical Journal (2003)
- Volume: 53, Issue: 2, page 225-240
- ISSN: 0011-4642
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topAlsardary, Salar Y., and Ali, Ali A.. "The basis number of some special non-planar graphs." Czechoslovak Mathematical Journal 53.2 (2003): 225-240. <http://eudml.org/doc/30772>.
@article{Alsardary2003,
abstract = {The basis number of a graph $G$ was defined by Schmeichel to be the least integer $h$ such that $G$ has an $h$-fold basis for its cycle space. He proved that for $m,n\ge 5$, the basis number $b(K_\{m,n\})$ of the complete bipartite graph $K_\{m,n\}$ is equal to 4 except for $K_\{6,10\}$, $K_\{5,n\}$ and $K_\{6,n\}$ with $n=5,6,7,8$. We determine the basis number of some particular non-planar graphs such as $K_\{5,n\}$ and $K_\{6,n\}$, $n=5,6,7,8$, and $r$-cages for $r=5,6,7,8$, and the Robertson graph.},
author = {Alsardary, Salar Y., Ali, Ali A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {graphs; basis number; cycle space; basis; graphs; basis number; cycle space; basis},
language = {eng},
number = {2},
pages = {225-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The basis number of some special non-planar graphs},
url = {http://eudml.org/doc/30772},
volume = {53},
year = {2003},
}
TY - JOUR
AU - Alsardary, Salar Y.
AU - Ali, Ali A.
TI - The basis number of some special non-planar graphs
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 225
EP - 240
AB - The basis number of a graph $G$ was defined by Schmeichel to be the least integer $h$ such that $G$ has an $h$-fold basis for its cycle space. He proved that for $m,n\ge 5$, the basis number $b(K_{m,n})$ of the complete bipartite graph $K_{m,n}$ is equal to 4 except for $K_{6,10}$, $K_{5,n}$ and $K_{6,n}$ with $n=5,6,7,8$. We determine the basis number of some particular non-planar graphs such as $K_{5,n}$ and $K_{6,n}$, $n=5,6,7,8$, and $r$-cages for $r=5,6,7,8$, and the Robertson graph.
LA - eng
KW - graphs; basis number; cycle space; basis; graphs; basis number; cycle space; basis
UR - http://eudml.org/doc/30772
ER -
References
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