Geodesic
Statuses and double branch weights of quadrangular outerplanar graphs
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 69 (2015) no. 1 Cet article a éte moissonné depuis la source Library of Science

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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.
Keywords: Centroid, median, outerplanar graph, status, tree 
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Bielak, Halina; Powroźnik, Kamil. Statuses and double branch weights of quadrangular outerplanar graphs. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 69 (2015) no. 1. http://geodesic.mathdoc.fr/item/AUM_2015_69_1_a6/

[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.