Geodesic
Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs
The electronic journal of combinatorics, Tome 15 (2008)
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In the paper "Broersma and Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444", the authors asked a 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.
DOI : 10.37236/755
Classification : 05C60, 05C75
Mots-clés : path graph, connected, isomorphism, triple of mutually nonisomorphic connected graphs, isomorphic connected \(P_3\)-graph, generalized \(K_{3,3}\)-type, Whitney type 
@article{10_37236_755,
     author = {Xueliang Li and Yan Liu},
     title = {Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected {\(P_{3}\)-graphs}},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/755},
     zbl = {1159.05040},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/755/}
}
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Xueliang Li; Yan Liu. Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/755

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