The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs - Grant Fickes; Wing Hong Tony Wong (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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 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.