id: 05703752
dt: j
an: 05703752
au: Li, Xiangwen; Mak, Vicky; Zhou, Sanming
ti: Optimal radio labellings of complete $m$-ary trees.
so: Discrete Appl. Math. 158, No. 5, 507-515 (2010).
py: 2010
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: channel assignment; radio labelling; radio number; $m$-ary tree; binary
    tree
ci: 
li: doi:10.1016/j.dam.2009.11.014
ab: Summary: A radio labelling of a connected graph $G$ is a mapping $f:V(G)
    \rightarrow \{0,1,2,\cdots \}$ such that $|f(u) - f(v)| \geq \text
    {diam}(G) - d(u,v) +1$ for each pair of distinct vertices $u,v \in
    V(G)$, where diam$(G)$ is the diameter of $G$ and $d(u,v)$ the distance
    between $u$ and $v$. The span of $f$ is defined as max$_{u,v \in V(G)}
    |f(u) - f(v)|$, and the radio number of $G$ is the minimum span of a
    radio labelling of $G$. A complete $m$-ary tree $(m \geq 2)$ is a
    rooted tree such that each vertex of degree greater than one has
    exactly $m$ children and all degree-one vertices are of equal distance
    (height) to the root. In this paper we determine the radio number of
    the complete $m$-ary tree for any $m\geq 2$ with any height and
    construct explicitly an optimal radio labelling.
rv: