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<item>
  <id>06092282</id>
  <dt>j</dt>
  <an>06092282</an>
  <augroup>
    <au>Alzoubi, Maref Y.M.</au>
  </augroup>
  <ti>The basis number of the Cartesian product of different ladders.</ti>
  <so>Ars Comb. 99, 89-95 (2011).</so>
  <py>2011</py>
  <pu>Charles Babbage Research Centre, Winnipeg, MB</pu>
  <lagroup>
    <la>EN</la>
  </lagroup>
  <ccgroup>
  </ccgroup>
  <utgroup>
    <ut>cycle basis</ut>
    <ut>ladder</ut>
    <ut>cartesian product</ut>
  </utgroup>
  <cigroup>
  </cigroup>
  <ligroup>
  </ligroup>
  <abgroup>
    <ab>The regular ladder with $n$ steps ($2n$ vertices and $3n - 2$ edges) will be denoted by $L_n$. Containing this ladder $L_n$ are the M\"{o}bius ladder $ML_n$ (with $2n$ vertices and $3n$ edges) and the Cycle ladder $CL_n$ (with $2n$ vertices and $3n$ edges). It is shown that the cycle basis number ($b$) of the cartesian product of any pair of the ladders $L_m, ML_n, CL_p$ for ($3 \leq m, n, p$) is at most $5$. More specifically, it is shown that the cycle basis is $4$ for the cartesian product of a Cycle ladder with any of the other ladders (M\"{o}bius, Cycle, Regular), and also $b(L_n \times ML_m) = b(ML_n \times ML_m) = 4$.</ab>
    <rv>3352</rv>
  </abgroup>
</item>