**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)**

#### Author = Moazzami, D.

Number of Articles: 21

##### A Survey on Tenacity Parameter\\Part II

*Volume 54, Issue 1 , June 2022, , Pages 47-72*

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**Abstract **

In this paper, we study the edge tenacity of graphs. We will be primarilyinterested in edge-tenacious graphs, which can be considered very stable and are somewhat analogous in edge tenacityto honest graphs in edge-integrity. We show several results about edge-tenacious graphs as well asfind numerous ...
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##### On the J-Tightness of Graphs

*Volume 53, Issue 2 , December 2021, , Pages 57-74*

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**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 ...
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##### A Survey on Tenacity Parameter\\Part I

*Volume 53, Issue 1 , June 2021, , Pages 181-196*

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**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 ...
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##### A note on the approximability of the tenacity of graphs

*Volume 52, Issue 2 , December 2020, , Pages 149-157*

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**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$\frac{1}{2} \left( \frac{n-1}{2} \right) ^{1-\epsilon}$.
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##### Edge-Tenacity

*Volume 52, Issue 1 , June 2020, , Pages 175-182*

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**Abstract **

The edge-tenacity $T_e(G)$ of a graph G was defined as\begin{center} $T_e(G)=\displaystyle \min_{F\subset E(G)}\{\frac{\mid F\mid +\tau(G-F)}{\omega(G-F)}\}$\end{center}where the minimum is taken over all edge cutset F of G. We defineG-F to be the graph induced by the edges of $E(G)-F$, $\tau(G-F)$is ...
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##### Tenacious Graph is NP-hard

*Volume 51, Issue 2 , December 2019, , Pages 127-134*

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**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 ...
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##### Tenacity and rupture degree parameters for trapezoid graphs

*Volume 51, Issue 1 , June 2019, , Pages 157-164*

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**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 ...
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##### Tenacity and some other Parameters of Interval Graphs can be computed in polynomial time

*Volume 50, issue 2 , December 2018, , Pages 81-87*

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**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 ...
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##### Vulnerability in Networks - A Survey

*Volume 50, Issue 1 , June 2018, , Pages 109-118*

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**Abstract **

The analysis of vulnerability in networks generally involves some questionsabout how the underlying graph is connected. One is naturally interestedin studying the types of disruption in the network that maybe causedby failures of certain links or nodes. In terms of a graph, the concept ofconnectedness ...
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##### Vulnerability Measure of a Network - a Survey

*Volume 49, Issue 2 , December 2017, , Pages 33-40*

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**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 ...
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##### Normalized Tenacity and Normalized Toughness of Graphs

*Volume 49, Issue 2 , December 2017, , Pages 141-159*

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**Abstract **

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters. Using these new parameters enables the graphs with different orders be comparable with each other regarding their ...
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##### Edge-tenacity in Networks

*Volume 49, Issue 1 , June 2017, , Pages 45-53*

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**Abstract **

Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between ...
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##### Tenacity and some related results

*Volume 49, Issue 1 , June 2017, , Pages 83-91*

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**Abstract **

Conceptually graph vulnerability relates to the study of graphintactness when some of its elements are removed. The motivation forstudying vulnerability measures is derived from design and analysisof networks under hostile environment. Graph tenacity has been anactive area of research since the the concept ...
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##### On the tenacity of cycle permutation graph

*Volume 48, Issue 1 , December 2016, , Pages 37-44*

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**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 ...
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##### An Optimization Model for Epidemic Mitigation and Some Theoretical and Applied Generalizations

*Volume 48, Issue 1 , December 2016, , Pages 99-116*

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**Abstract **

In this paper, we present a binary-linear optimization model to prevent the spread of an infectious disease in a community. The model is based on the remotion of some connections in a contact network in order to separate infected nodes from the others. By using this model we nd an exact optimal solution ...
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##### Towards a measure of vulnerability, tenacity of a Graph

*Volume 48, Issue 1 , December 2016, , Pages 149-153*

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**Abstract **

If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including ...
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##### Online Scheduling of Jobs for D-benevolent instances On Identical Machines

*Volume 47, Issue 1 , June 2016, , Pages 27-36*

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**Abstract **

We consider online scheduling of jobs with specic release time on m identical machines. Each job has a weight and a size; the goal is maximizing total weight of completed jobs. At release time of a job it must immediately be scheduled on a machine or it will be rejected. It is also allowed during execution ...
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##### Heuristic and exact algorithms for Generalized Bin Covering Problem

*Volume 47, Issue 1 , June 2016, , Pages 53-62*

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**Abstract **

In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the ...
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##### Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model

*Volume 47, Issue 1 , June 2016, , Pages 79-92*

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**Abstract **

In this paper we restrict every set splitting problem to the special case in which every set has just three elements. This restricted version is also NP-complete. Then, we introduce a general conversion from any set splitting problem to 3-set splitting. Then we introduce a randomize algorithm, and we ...
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##### A Cellular Automaton Based Algorithm for Mobile Sensor Gathering

*Volume 47, Issue 1 , June 2016, , Pages 93-99*

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**Abstract **

In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors ...
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##### Toughness of the Networks with Maximum Connectivity

*Volume 46, Issue 1 , December 2015, , Pages 51-71*