Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak; Kamil Powroźnik

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2015)

  • Volume: 69, Issue: 1
  • ISSN: 0365-1029

Abstract

top
In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.

How to cite

top

Halina Bielak, and Kamil Powroźnik. "Statuses and double branch weights of quadrangular outerplanar graphs." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 69.1 (2015): null. <http://eudml.org/doc/289778>.

@article{HalinaBielak2015,
abstract = {In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.},
author = {Halina Bielak, Kamil Powroźnik},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Centroid; median; outerplanar graph; status; tree},
language = {eng},
number = {1},
pages = {null},
title = {Statuses and double branch weights of quadrangular outerplanar graphs},
url = {http://eudml.org/doc/289778},
volume = {69},
year = {2015},
}

TY - JOUR
AU - Halina Bielak
AU - Kamil Powroźnik
TI - Statuses and double branch weights of quadrangular outerplanar graphs
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2015
VL - 69
IS - 1
SP - null
AB - In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.
LA - eng
KW - Centroid; median; outerplanar graph; status; tree
UR - http://eudml.org/doc/289778
ER -

References

top
  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Application, Macmillan London and Elsevier, New York, 1976. 
  2. Entringer, R. C., Jackson, D. E., Snyder, D. A., Distance in graphs, Czech. Math. J. 26 (1976), 283–296. 
  3. Jordan, C., Sur les assembblages des lignes, J. Reine Angnew. Math. 70 (1896), 185–190. 
  4. Kang, A. N. C., Ault, D. A., Some properties of a centroid of a free tree, Inform. Process. Lett. 4, No. 1 (1975), 18–20. 
  5. Kariv, O., Hakimi, S. L., An algorithmic approach to network location problems. II: The p-medians, SIAM J. Appl. Math. 37 (1979), 539–560. 
  6. Korach, E., Rotem, D., Santoro, N., Distributed algorithms for finding centers and medians in networks, ACM Trans. on Programming Languages and Systems 6, No. 3 (1984), 380–401. 
  7. Lin, Ch., Shang, J-L., Statuses and branch-weights of weighted trees, Czech. Math. J. 59 (134) (2009), 1019–1025. 
  8. Lin, Ch., Tsai, W-H., Shang, J-L., Zhang, Y-J., Minimum statuses of connected graphs with fixed maximum degree and order, J. Comb. Optim. 24 (2012), 147–161. 
  9. Mitchell, S. L., Another characterization of the centroid of a tree, Discrete Math. 23 (1978), 277–280. 
  10. Proskurowski, A., Centers of 2-trees, Ann. Discrete Math. 9 (1980), 1–5. 
  11. Slater, P. J., Medians of arbitrary graphs, J. Graph Theory 4 (1980), 289–392. 
  12. Szamkołowicz, L., On problems related to characteristic vertices of graphs, Colloq. Math. 42 (1979), 367–375. 
  13. Truszczynski, M., Centers and centroids of unicyclic graphs, Math. Slovaka 35 (1985), 223–228. 
  14. Zelinka, B., Medians and peripherians of trees, Arch. Math. (Brno) 4, No. 2 (1968), 87–95. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.