Li, Xueliang; Liu, Yan Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs. (English) Zbl 1159.05040 Electron. J. Comb. 15, No. 1, Research Paper R31, 8 p. (2008). Summary: In the paper “Path graphs”, H.J. Broersma and C. Hoede [J. Graph Theory 13, No.4, 427–444 (1989; Zbl 0677.05068)] posed the problem whether there is a triple of mutually nonisomorphic connected graphs which have an isomorphic connected \(P_3\)-graph. In this paper, we show that there is no such triple, and thus completely solve this problem. MSC: 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C75 Structural characterization of families of graphs Keywords:path graph; connected; isomorphism; triple of mutually nonisomorphic connected graphs; isomorphic connected \(P_3\)-graph; generalized \(K_{3,3}\)-type; Whitney type Citations:Zbl 0677.05068 PDFBibTeX XMLCite \textit{X. Li} and \textit{Y. Liu}, Electron. J. Comb. 15, No. 1, Research Paper R31, 8 p. (2008; Zbl 1159.05040) Full Text: arXiv EuDML EMIS