On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs

• Autorzy: Dingguo Wang , Erfang Shan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

4-regular graph; claw-free; cut-vertices; end-blocks

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 127-136

Daty

wydano

2014-02-01

online

2014-02-14

Twórcy

autor

Dingguo Wang

• Department of Mathematics, Shanghai University, Shanghai 200444, China
• College of Mathematics Science, Chongqing Normal University Chongqing 400047, China

autor

Erfang Shan

• School of Management, Shanghai University, Shanghai 200444, China 2Department of Mathematics, Shanghai University, Shanghai 200444, China

Bibliografia

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• [5] N. Achuthan and A.R. Rao, On the number of cut edges in a regular graph, Australas. J. Combin. 27 (2003) 5-12.
• [6] A. Ramachandra Rao, An extremal problem in graph theory, Israel J. Math. 6 (1968) 261-266. doi:10.1007/BF02760258[Crossref]
• [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]

Identyfikatory

DOI

10.7151/dmgt.1724