"During our research discussion , we discovered a graph G that has exactly one basis-forced vertex 'u' (i.e., every metric basis of G contains u). We are interested in understanding the impact of this property on the structure of the graph."
James Tuite
Have you seen this paper? Hakanen, Anni, Ville Junnila, Tero Laihonen, and Ismael G. Yero. "On vertices contained in all or in no metric basis." Discrete Applied Mathematics 319 (2022): 407-423.
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SIMON RAJ F
Dear James, I red the research article , i found examples of graphs with two basis forced vertex but not found any result related to graph with only one basis forced vertex.
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