Minimum 3-geodetically connected graphs

  • Authors:

  • Martina Bosíková

  • Affiliations:

  • Department of Numerical and Optimization Methods, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 84248 Bratislava, Slovakia

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2003

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Abstract

A graph G is k-geodetically connected (k-GC) if it is connected and the removal of at least k vertices is required to increase the distance between at least one pair of vertices or reduce G to a single vertex. We completely characterize the class of minimum 3-GC graphs that have the fewest edges for a given number of vertices.