On the rainbow vertex connection number of general unicyclic graphs
Ridho Alfarisi, Arika Indah Kristiana, Sharifah Kartini Said Husain · Journal of Discrete Mathematical Sciences and Cryptography · 2026
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.