Characterizing Block Graphs in Terms of One-vertex Extensions

Lilian Markenzon, Christina Fraga Esteves Maciel Waga


Block graphs has been extensively studied for many decades. In this paper we present a new characterization of the class in terms of one-vertex extensions. To this purpose, a specific representation based on the concept of boundary cliques is presented, bringing about some properties of the graph.


block graph, one-vertex-extension

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F. Harary, “A characterization of block graphs,” Canadian Mathematical Bul- letin, vol. 6, no. 1, pp. 1–6, 1963.

E. Howorka, “On metric properties of certain clique graphs,” Journal of Com- binatorial Theory, Series B, vol. 27, pp. 67–74, 1979.

H.-J. Bandelt and H. M. Mulder, “Three interval conditions for graphs,” Ars Combinatoria, vol. 29B, pp. 213–223, 1990.

A. Behtoei, M. Jannesari, and B. Taeri, “A characterization of block graphs,” Discrete Applied Mathematics, vol. 158, pp. 219–221, 2010.

H.-J. Bandelt and H. M. Mulder, “Distance-hereditary graphs,” Journal of Combinatorial Theory, Series B, vol. 41, pp. 182–208, 1986.

H. Mulder and L. Nebeský, “Leaps: an approach to the block structure of a graph,” Discussiones Mathematicae Graph Theory, vol. 26, pp. 77–90, 2006.

A. Dress, K. Huber, J. Koolen, V. Moulton, and A. Spillner, “Characterizing block graphs in terms of their vertex-induced partitions,” Australasian Journal of Combinatorics, vol. 66, no. 1, pp. 1–9, 2016.

H. Mulder, “An observation on block graphs,” Bulletin of the Institute of Com- binatorics and its Applications, vol. 77, pp. 57–58, 2016.

J. R. S. Blair and B. Peyton, “An introduction to chordal graphs and clique trees,” In Graph Theory and Sparse Matrix Computation, IMA, vol. 56, pp. 1– 29, 1993.

M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. New York: Academic Press, 2 ed., 2004.

L. Markenzon, P. R. C. Pereira, C. F. E. M. Waga, C. V. P. Friedmann, and A. Lozano, “An efficient representation of chordal graphs,” Operations Research Letters, vol. 41, pp. 331–335, 2013.

D. J. Rose, R. E. Tarjan, and G. Lueker, “Algorithmic aspects of vertex elimination on graphs,” SIAM Journal on Computing, vol. 5, pp. 266–283, 1976.


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