Computing rupture degrees of some graphs

  • Authors:

  • Fengwei Li;Qingfang Ye;Baohuai Sheng

  • Affiliations:

  • Department of mathematics, Shaoxing University, Shaoxing, Zhejiang, P. R. China;Department of mathematics, Shaoxing University, Shaoxing, Zhejiang, P. R. China;Department of mathematics, Shaoxing University, Shaoxing, Zhejiang, P. R. China

  • Venue:
  • WSEAS Transactions on Mathematics
  • Year:
  • 2012

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Abstract

Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructed when they do get disrupted. These desirable properties of networks can be measured by various parameters such as connectivity, toughness, tenacity and rupture degree. Among these parameters, rupture degree is comparatively better parameter to measure the vulnerability of networks. In this paper, the authors give the exact values for the rupture degree of the Cartesian product of a path and a cycle. After that, we discuss the rupture degree of total graphs of paths and cycles. Finally, we study the values for rupture degree of powers of paths and cycles.