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\iteman{io-port 05703752}
\itemau{Li, Xiangwen; Mak, Vicky; Zhou, Sanming}
\itemti{Optimal radio labellings of complete $m$-ary trees.}
\itemso{Discrete Appl. Math. 158, No. 5, 507-515 (2010).}
\itemab
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.
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\itemut{channel assignment; radio labelling; radio number; $m$-ary tree; binary tree}
\itemli{doi:10.1016/j.dam.2009.11.014}
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