Strong geodetic number of complete bipartite graphs, crown graphs and hypercubes

Valentin Gledel; Vesna Iršič

Strong geodetic number of complete bipartite graphs, crown graphs and hypercubes

Combinatorics 2018-10-10 v1

Authors: Valentin Gledel , Vesna Iršič

Abstract

The strong geodetic number, $\text{sg}(G),$ of a graph $G$ is the smallest number of vertices such that by fixing one geodesic between each pair of selected vertices, all vertices of the graph are covered. In this paper, the study of the strong geodetic number of complete bipartite graphs is continued. The formula for $\text{sg}(K_{n,m})$ is given, as well as a formula for the crown graphs $S_n^0$ . Bounds on $\text{sg}(Q_n)$ are also discussed.

Keywords

strong geodetic number complete bipartite graph crown graph hypercube geodesic

Cite

@article{arxiv.1810.04004,
  title  = {Strong geodetic number of complete bipartite graphs, crown graphs and hypercubes},
  author = {Valentin Gledel and Vesna Iršič},
  journal= {arXiv preprint arXiv:1810.04004},
  year   = {2018}
}

Comments

13 pages, 1 figure, 1 table

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