English

Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected $P_3$-graphs

Combinatorics 2007-11-26 v1

Abstract

In the paper "Broersma and Hoede, {\it Path graphs}, J. Graph Theory {\bf 13} (1989) 427-444", the authors proposed a problem whether there is a triple of mutually nonisomorphic connected graphs which have an isomorphic connected P3P_3-graph. For a long time, this problem remains unanswered. In this paper, we give it a negative answer that there is no such triple, and thus completely solve this problem.

Keywords

Cite

@article{arxiv.0711.3677,
  title  = {Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected $P_3$-graphs},
  author = {Xueliang Li and Yan Liu},
  journal= {arXiv preprint arXiv:0711.3677},
  year   = {2007}
}

Comments

9 pages