The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs
Grant Fickes, Tony W. H. Wong · Electronic Journal of Graph Theory and Applications · 2022
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.