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arXiv · 2102.07576

The Edge-Distinguishing Chromatic Number of Petal Graphs, Chorded Cycles, and Spider Graphs

Grant Fickes·Wing Hong Tony Wong
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Abstract

The edge-distinguishing chromatic number (EDCN) of a graph $G$ is the minimum positive integer $k$ such that there exists a vertex coloring $c:V(G)\to\{1,2,\dotsc,k\}$ 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.

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Grant Fickes, Wing Hong Tony Wong. 2021-02-15. The Edge-Distinguishing Chromatic Number of Petal Graphs, Chorded Cycles, and Spider Graphs. https://doi.org/10.5614/ejgta.2022.10.2.5

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