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

Grant Fickes (Department of Mathematics, University of South Carolina, USA)
Wing Hong Tony Wong (Department of Mathematics, Kutztown University of Pennsylvania, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications

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.