Extreme Tenacity of Graphs with Given Order and Size

T. C.E. Cheng, Yin Kui Li, Chuan Dong Xu, Sheng Gui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured by various graph parameters, such as connectivity, toughness, scattering number, integrity, tenacity, rupture degree and edge-analogues of some of them. Among these parameters, the tenacity and rupture degree are two better ones to measure the stability of a network. In this paper, we consider two extremal problems on the tenacity of graphs: determine the minimum and maximum tenacity of graphs with given order and size. We give a complete solution to the first problem, while for the second one, it turns out that the problem is much more complicated than that of the minimum case. We determine the maximum tenacity of trees with given order and show the corresponding extremal graphs. The paper concludes with a discussion of a related problem on the edge vulnerability parameters of graphs.
Original languageEnglish
Pages (from-to)307-315
Number of pages9
JournalJournal of the Operations Research Society of China
Issue number3
Publication statusPublished - 1 Sep 2014


  • Maximum tenacity
  • Minimum tenacity
  • Trees
  • Vulnerability parameters

ASJC Scopus subject areas

  • Decision Sciences(all)

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