The basis number of some special non-planar graphs

Title:

The basis number of some special non-planar graphs

Creator:

Alsardary, Salar Y. and Ali, Ali A.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:daff075f-8220-4415-8bae-500dcb1aa464
uuid:daff075f-8220-4415-8bae-500dcb1aa464

Subject:

graphs, basis number, cycle space, and basis

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

225-240

Source:

Czechoslovak Mathematical Journal | 2003 Volume:53 | Number:2

Harvested from:

CDK

Metadata only:

false