Connectivity of path graphs

Martin Knor; L'udovít Niepel

Discussiones Mathematicae Graph Theory (2000)

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

Abstract

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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.

How to cite

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Martin 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

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  1. [1] A. Belan and P. Jurica, Diameter in path graphs, Acta Math. Univ. Comenian. LXVIII (1999) 111-126. Zbl0929.05024
  2. [2] H.J. Broersma and C. Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444, doi: 10.1002/jgt.3190130406. Zbl0677.05068
  3. [3] M. Knor and L'. Niepel, Path, trail and walk graphs, Acta Math. Univ. Comenian. LXVIII (1999) 253-256. Zbl0942.05033
  4. [4] M. Knor and L'. Niepel, Distances in iterated path graphs, Discrete Math. (to appear). 
  5. [5] M. Knor and L'. Niepel, Centers in path graphs, (submitted). 
  6. [6] M. Knor and L'. Niepel, Graphs isomorphic to their path graphs, (submitted). 
  7. [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. [8] X. Li and B. Zhao, Isomorphisms of P₄-graphs, Australasian J. Combin. 15 (1997) 135-143. Zbl0878.05061
  9. [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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