On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs
Dingguo Wang ; Erfang Shan
Discussiones Mathematicae Graph Theory, Tome 34 (2014), p. 127-136 / Harvested from The Polish Digital Mathematics Library
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A cut-vertex in a graph G is a vertex whose removal increases the number of connected components of G. An end-block of G is a block with a single cut-vertex. In this paper we establish upper bounds on the numbers of end-blocks and cut-vertices in a 4-regular graph G and claw-free 4-regular graphs. We characterize the extremal graphs achieving these bounds.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267975 
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Dingguo Wang; Erfang Shan. On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 127-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1724/

[1] M.O. Albertson and D.M. Berman, The number of cut-vertices in a graph of given minimum degree, Discrete Math. 89 (1991) 97-100. doi:10.1016/0012-365X(91)90402-N[Crossref]

[2] B. Bollobás, Modern Graph Theory (New York, Springer-Verlag, 2001).

[3] L.H. Clark and R.C. Entringer, The number of cut vertices in graphs with given minimum degree, Discrete Math. 18 (1990) 137-145. doi:10.1016/0012-365X(90)90145-8[Crossref]

[4] K. Nirmala and A.R. Rao, The number of cut vertices in a regular graph, Cahiers Centre Etudes Reserche Oper. 17 (1975) 295-299. | Zbl 0321.05138

[5] N. Achuthan and A.R. Rao, On the number of cut edges in a regular graph, Australas. J. Combin. 27 (2003) 5-12. | Zbl 1021.05055

[6] A. Ramachandra Rao, An extremal problem in graph theory, Israel J. Math. 6 (1968) 261-266. doi:10.1007/BF02760258[Crossref] | Zbl 0174.55201

[7] A. Ramachandra Rao, Some extremal problems and characterizations in the theory of graphs, Ph.D. Thesis, Indian Statistical Institute (1969).

[8] S.B. Rao, Contributions to the theory of directed and undirected graphs, Ph.D. Thesis, Indian Statistical Institute (1970).

[9] O. Suil and D.B. West, Balloons, cut-edges, matchings, and total domination in regular graphs of odd degree, J. Graph Theory 64 (2010) 116-131. doi:10.1002/jgt.20443 [WoS][Crossref] | Zbl 1201.05049