Volume 55 (2023)
Volume 54 (2022)
Volume 53 (2021)
Volume 52 (2020)
Volume 51 (2019)
Volume 50 (2018)
Volume 49 (2017)
Volume 48 (2016)
Volume 47 (2016)
Volume 46 (2015)
Volume 45 (2014)
Volume 44 (2013)
Volume 43 (2009)
Volume 42 (2008)
Volume 41 (2007)
Keywords = Tenacity
Number of Articles: 11
On the J-Tightness of Graphs
Articles in Press, Accepted Manuscript, Available Online from 14 January 2022
Abstract
We introduce a new invariant vulnerability parameter named “J-Tightness” or “J(G)” for graphs. As a stability measure, its properties along with comparisons to other parameters of a graph are proposed. We show how it is calculated for complete graphs and cycles. We show that J-Tightness ... Read MoreOn the J-Tightness of Graphs
Volume 53, Issue 2 , December 2021, , Pages 57-74
Abstract
We introduce a new invariant vulnerability parameter named “J-Tightness” or “J(G)” for graphs. As a stability measure, its properties along with comparisons to other parameters of a graph are proposed. We show how it is calculated for complete graphs and cycles. We show that J-Tightness ... Read MoreA Survey on Tenacity Parameter\\Part I
Volume 53, Issue 1 , June 2021, , Pages 181-196
Abstract
If we think of the graph as modeling a network, the vulnerability measurethe resistance of the network to disruption of operation after the failure of certainstations or communication links. In assessing the "vulnerability"of a graph one determines the extent to which the graph retains certainproperties ... Read MoreA note on the approximability of the tenacity of graphs
Volume 52, Issue 2 , December 2020, , Pages 149-157
Abstract
In this paper we show that, if $NP\neq ZPP$, for any $\epsilon > 0$, the tenacity of graphwith $n$ vertices is not approximable in polynomial time within a factor of$\frac{1}{2} \left( \frac{n-1}{2} \right) ^{1-\epsilon}$. Read MoreTenacious Graph is NP-hard
Volume 51, Issue 2 , December 2019, , Pages 127-134
Abstract
The tenacity of a graph $G$, $T(G)$, is defined by$T(G) = min\{\frac{\mid S\mid +\tau(G-S)}{\omega(G-S)}\}$, where theminimum is taken over all vertex cutsets $S$ of $G$. We define$\tau(G - S)$ to be the number of the vertices in the largestcomponent of the graph $G-S$, and $\omega(G-S)$ be the number ... Read MoreTenacity and rupture degree parameters for trapezoid graphs
Volume 51, Issue 1 , June 2019, , Pages 157-164
Abstract
Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs ... Read MoreTenacity and some other Parameters of Interval Graphs can be computed in polynomial time
Volume 50, issue 2 , December 2018, , Pages 81-87
Abstract
In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters ... Read MoreVulnerability Measure of a Network - a Survey
Volume 49, Issue 2 , December 2017, , Pages 33-40
Abstract
In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity. Since we are primarily interested in the case where ... Read MoreOn the tenacity of cycle permutation graph
Volume 48, Issue 1 , December 2016, , Pages 37-44
Abstract
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn( α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation ... Read MoreA Survey on Stability Measure of Networks
Volume 48, Issue 1 , December 2016, , Pages 141-148
Abstract
In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity. Read MoreA Survey On the Vulnerability Parameters of Networks
Volume 48, Issue 1 , December 2016, , Pages 155-162