  The edge-distinguishing chromatic number (EDCN) of a graph $G$ is the minimum
positive integer $k$ such that there exists a vertex coloring
$c:V(G)\to\{1,2,\dotsc,k\}$ whose induced edge labels $\{c(u),c(v)\}$ are
distinct for all edges $uv$. Previous work has determined the EDCN of paths,
cycles, and spider graphs with three legs. In this paper, we determine the EDCN
of petal graphs with two petals and a loop, cycles with one chord, and spider
graphs with four legs. These are achieved by graph embedding into looped
complete graphs.
