Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs (Q1010739)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs |
scientific article |
Statements
Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected \(P_{3}\)-graphs (English)
0 references
7 April 2009
0 references
Summary: In the paper ``Path graphs'', \textit{H.J. Broersma} and \textit{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.
0 references
path graph
0 references
connected
0 references
isomorphism
0 references
triple of mutually nonisomorphic connected graphs
0 references
isomorphic connected \(P_3\)-graph
0 references
generalized \(K_{3,3}\)-type
0 references
Whitney type
0 references
