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Cyclic Vertex Connectivity of Star Graphs

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Combinatorial Optimization and Applications (COCOA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6508))

Abstract

For a connected graph G, a vertex subset F ⊂ V(G) is a cyclic vertex-cut of G if G − F is disconnected and at least two of its components contain cycles. The cardinality of a minimum cyclic vertex-cut of G, denoted by κ c (G), is the cyclic vertex-connectivity of G. In this paper, we show that for any integer n ≥ 4, the n-dimensional star graph SG n has κ c (SG n ) = 6(n − 3).

This research is supported by NSFC (10971255), the Key Project of Chinese Ministry of Education (208161), Program for New Century Excellent Talents in University, and The Project-sponsored by SRF for ROCS, SEM.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China

    Zhihua Yu, Qinghai Liu & Zhao Zhang

Authors
  1. Zhihua Yu
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  2. Qinghai Liu
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  3. Zhao Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Weili Wu  & Ovidiu Daescu  & 

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Yu, Z., Liu, Q., Zhang, Z. (2010). Cyclic Vertex Connectivity of Star Graphs. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-17458-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17457-5

  • Online ISBN: 978-3-642-17458-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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