# Connectivity of path graphs

Discussiones Mathematicae Graph Theory (2000)

- Volume: 20, Issue: 2, page 181-195
- ISSN: 2083-5892

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topMartin Knor, and L'udovít Niepel. "Connectivity of path graphs." Discussiones Mathematicae Graph Theory 20.2 (2000): 181-195. <http://eudml.org/doc/270291>.

@article{MartinKnor2000,

abstract = {We prove a necessary and sufficient condition under which a connected graph has a connected P₃-path graph. Moreover, an analogous condition for connectivity of the Pₖ-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.},

author = {Martin Knor, L'udovít Niepel},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {connectivity; path graph; cycle; path graphs; connected graph},

language = {eng},

number = {2},

pages = {181-195},

title = {Connectivity of path graphs},

url = {http://eudml.org/doc/270291},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Martin Knor

AU - L'udovít Niepel

TI - Connectivity of path graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2000

VL - 20

IS - 2

SP - 181

EP - 195

AB - We prove a necessary and sufficient condition under which a connected graph has a connected P₃-path graph. Moreover, an analogous condition for connectivity of the Pₖ-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.

LA - eng

KW - connectivity; path graph; cycle; path graphs; connected graph

UR - http://eudml.org/doc/270291

ER -

## References

top- [1] A. Belan and P. Jurica, Diameter in path graphs, Acta Math. Univ. Comenian. LXVIII (1999) 111-126. Zbl0929.05024
- [2] H.J. Broersma and C. Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444, doi: 10.1002/jgt.3190130406. Zbl0677.05068
- [3] M. Knor and L'. Niepel, Path, trail and walk graphs, Acta Math. Univ. Comenian. LXVIII (1999) 253-256. Zbl0942.05033
- [4] M. Knor and L'. Niepel, Distances in iterated path graphs, Discrete Math. (to appear).
- [5] M. Knor and L'. Niepel, Centers in path graphs, (submitted).
- [6] M. Knor and L'. Niepel, Graphs isomorphic to their path graphs, (submitted).
- [7] H. Li and Y. Lin, On the characterization of path graphs, J. Graph Theory 17 (1993) 463-466, doi: 10.1002/jgt.3190170403. Zbl0780.05048
- [8] X. Li and B. Zhao, Isomorphisms of P₄-graphs, Australasian J. Combin. 15 (1997) 135-143. Zbl0878.05061
- [9] X. Yu, Trees and unicyclic graphs with Hamiltonian path graphs, J. Graph Theory 14 (1990) 705-708, doi: 10.1002/jgt.3190140610. Zbl0743.05018

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