A result on $K$(2,1)Total choosability of planar graphs 
Received:March 14, 2021 Revised:November 24, 2021 
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$L$(2,1)total labeling $k$(2,1)total choosable planar graphs

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Abstract: 
A list assignment of a graph $G$ is a function $L:V(G)\cup E(G)\rightarrow 2^{N}$. A graph $G$ is $L$(2,1)Total labeling if there exists a function $c$ such that $c(x)\in L(x)$ for all $x\in V(G)\cup E(G)$, $c(u)c(v)\geq 1$ if $uv\in E(G)$, $c(e_{1})c(e_{2})\geq 1$ if the edges $e_{1}$ and $e_{2}$ are adjacent, and $c(u)c(e)\geq 2$ if the vertex $u$ is incident to the edge $e$.A graph $G$ is $k$(2,1)Total choosable if G is $L$(2,1)Total labeling for every list assignment $L$ provided that $L(x)=k,x\in V(G)\cup E(G)$. The $(2,1)$Total choice number of $G$, denoted by $C_{(2,1)}^{T}$, is the minimum $k$ such that $G$ is $k$(2,1)Total choosable.
In this paper, we prove that if $G$ is a planar graph with $\Delta(G)\geq 11$, then $C_{(2,1)}^{T}(G)\leq\Delta+4$. 
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