2024
DOI: 10.7151/dmgt.2469
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Approximate and exact results for the harmonious chromatic number

Abstract: Graph coloring is a fundamental topic in graph theory that requires an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring such that for every two distinct colors i, j at most one pair of adjacent vertices are colored with i and j. This type of coloring is edgedistinguishing and has potential applications in transportation networks, computer networks, airway network systems.The results presented … Show more

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