@techreport{TR-IC-17-13,
   number = {IC-17-13},
   author = {Atilio G. Luiz and C. N. Campos and R. Bruce Richter},
   title = {{On 0-rotatable caterpillars with diameter at least 7}},
   month = {August},
   year = {2017},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 05 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       A  graceful labelling of a tree $T$ is an injective function $f
       \colon  V(T)  \to \{0,\ldots,|E(T)|\}$ such that $\{|f(u)-f(v)|
       \colon uv \in E(T)\} = \{1,\ldots,|E(T)|\}$. A tree $T$ is said
       to  be  0-rotatable  if,  for each $v \in V(T)$, there exists a
       graceful  labelling  $f$  of  $T$ such that $f(v) = 0$. In this
       work,   it  is  proved  that  if  $T$  is  a  caterpillar  with 
       $diam(T)\geq  7$  and,  for every non-leaf vertex $v \in V(T)$,
       the   number   of   leaves   adjacent   to   $v$  is  at  least 
       $2+2((diam(T)-1)\bmod{2})$,  then  $T$  is  $0$-rotatable. This
       result  reinforces  the  conjecture that every caterpillar with
       diameter at least five is 0-rotatable.
  }
}