  Inspired by the phenomenon of co-channel interference in communication
network, a novel graph parameter, called $r$-vertex-strongly-distinguishing
total coloring (abbreviate as $D(r)$-VSDTC), is proposed in this paper. Given a
graph $G$, an $r$-VSDTC is an assignment of $k$ colors to $V(G)\cup E(G)$ such
that any two adjacent or incident elements receive different colors and any two
vertices with distance at most $r$ have distinct color-set, where the color-set
of a vertex $u$ is the set of colors assigned on $u$ and its neighborhoods and
incident edges. The \emph{$r$-vertex-strongly-distinguishing total chromatic
number} of $G$, denoted by $\chi_{r-vsdt}(G)$, is the minimum integer $k$ for
which $G$ admits a $k$-$D(r)$-VSDTC. We show that $\chi_{1-vsdt}(G)\leq
4\Delta(G)$ for every graph $G$ without isolated edges and $\chi_{1-vsdt}(G)\le
k\Delta(G)+3$ for a $k$-degenerated graph $G$ without isolated edges, where
$1\le k\le 3$.
