Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak; Kamil Powroźnik

Annales UMCS, Mathematica (2015)

  • Volume: 69, Issue: 1, page 5-21
  • ISSN: 2083-7402

Abstract

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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

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Halina Bielak, and Kamil Powroźnik. "Statuses and double branch weights of quadrangular outerplanar graphs." Annales UMCS, Mathematica 69.1 (2015): 5-21. <http://eudml.org/doc/271006>.

@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 UMCS, Mathematica},
keywords = {and phrases Centroid; median; outerplanar graph; status; tree; centroid},
language = {eng},
number = {1},
pages = {5-21},
title = {Statuses and double branch weights of quadrangular outerplanar graphs},
url = {http://eudml.org/doc/271006},
volume = {69},
year = {2015},
}

TY - JOUR
AU - Halina Bielak
AU - Kamil Powroźnik
TI - Statuses and double branch weights of quadrangular outerplanar graphs
JO - Annales UMCS, Mathematica
PY - 2015
VL - 69
IS - 1
SP - 5
EP - 21
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 - and phrases Centroid; median; outerplanar graph; status; tree; centroid
UR - http://eudml.org/doc/271006
ER -

References

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  1. [1] Bondy, J. A., Murty, U. S. R., Graph Theory with Application, Macmillan London and Elsevier, New York, 1976. Zbl1226.05083
  2. [2] Entringer, R. C., Jackson, D. E., Snyder, D. A., Distance in graphs, Czech. Math. J. 26 (1976), 283-296. Zbl0329.05112
  3. [3] Jordan, C., Sur les assembblages des lignes, J. Reine Angnew. Math. 70 (1896), 185-190. 
  4. [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. Zbl0313.68032
  5. [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. Zbl0432.90075
  6. [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. Zbl0543.68051
  7. [7] Lin, Ch., Shang, J-L., Statuses and branch-weights of weighted trees, Czech. Math. J. 59 (134) (2009), 1019-1025. Zbl1224.05148
  8. [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. Zbl1282.90216
  9. [9] Mitchell, S. L., Another characterization of the centroid of a tree, Discrete Math. 23 (1978), 277-280. Zbl0402.05019
  10. [10] Proskurowski, A., Centers of 2-trees, Ann. Discrete Math. 9 (1980), 1-5. Zbl0449.05018
  11. [11] Slater, P. J., Medians of arbitrary graphs, J. Graph Theory 4 (1980), 289-392. Zbl0446.05029
  12. [12] Szamkołowicz, L., On problems related to characteristic vertices of graphs, Colloq. Math. 42 (1979), 367-375. Zbl0437.05034
  13. [13] Truszczyński, M., Centers and centroids of unicyclic graphs, Math. Slovaka 35 (1985), 223-228. Zbl0585.05030
  14. [14] Zelinka, B., Medians and peripherians of trees, Arch. Math. (Brno) 4, No. 2 (1968), 87-95. Zbl0206.26105

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