
doi: 10.47974/jdmsc-2599
In a graph G, the distance between any two vertices is defined as the length of the shortest path connecting them. A path in G is termed rainbow vertex-connected if all internal vertices along the path have distinct colors. For every pair of vertices u and v in G, if there exists such a colored u-v path, the graph is considered rainbow vertex-connected. The minimum number of colors required to ensure that a connected graph G satisfies this condition is called the rainbow vertex-connection number, denoted by rvc(G). This study focuses on analyzing the rainbow vertex-connection number specifically for unicyclic graphs.
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