Statuses and double branch weights of quadrangular outerplanar graphs
Halina Bielak ; Kamil Powroźnik
Annales UMCS, Mathematica, Tome 68 (2015), p. 5-21 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:271006
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     author = {Halina Bielak and Kamil Powro\'znik},
     title = {Statuses and double branch weights of quadrangular outerplanar graphs},
     journal = {Annales UMCS, Mathematica},
     volume = {68},
     year = {2015},
     pages = {5-21},
     zbl = {1320.05028},
     language = {en},
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Halina Bielak; Kamil Powroźnik. Statuses and double branch weights of quadrangular outerplanar graphs. Annales UMCS, Mathematica, Tome 68 (2015) pp. 5-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0010/

[1] Bondy, J. A., Murty, U. S. R., Graph Theory with Application, Macmillan London and Elsevier, New York, 1976. | Zbl 1226.05083

[2] Entringer, R. C., Jackson, D. E., Snyder, D. A., Distance in graphs, Czech. Math. J. 26 (1976), 283-296. | Zbl 0329.05112

[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. | Zbl 0313.68032

[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. | Zbl 0432.90075

[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. | Zbl 0543.68051

[7] Lin, Ch., Shang, J-L., Statuses and branch-weights of weighted trees, Czech. Math. J. 59 (134) (2009), 1019-1025. | Zbl 1224.05148

[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. | Zbl 1282.90216

[9] Mitchell, S. L., Another characterization of the centroid of a tree, Discrete Math. 23 (1978), 277-280. | Zbl 0402.05019

[10] Proskurowski, A., Centers of 2-trees, Ann. Discrete Math. 9 (1980), 1-5. | Zbl 0449.05018

[11] Slater, P. J., Medians of arbitrary graphs, J. Graph Theory 4 (1980), 289-392. | Zbl 0446.05029

[12] Szamkołowicz, L., On problems related to characteristic vertices of graphs, Colloq. Math. 42 (1979), 367-375. | Zbl 0437.05034

[13] Truszczyński, M., Centers and centroids of unicyclic graphs, Math. Slovaka 35 (1985), 223-228. | Zbl 0585.05030

[14] Zelinka, B., Medians and peripherians of trees, Arch. Math. (Brno) 4, No. 2 (1968), 87-95. | Zbl 0206.26105