### The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs

#### Abstract

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*)→{1, 2, …, *k*} whose induced edge labels {*c*(*u*),*c*(*v*)} are distinct for all edges *u**v*. 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.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.5

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