Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined t...

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, tenacity and rupture degree are comparatively bet...

In this note, we show that one of the arguments used by Moazzami for computing the tenacity of the third Harary graph is wrong and then improve the proof. © 2014 Published by Elsevier B.V.

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 at least some nodes. Two well-known measures that indicate how "reliable" a graph is are the...

yarn tenacity is one of the most important properties in yarn production. this paper addresses modeling of yarn tenacity as well as optimally determining the amounts of the effective inputs to produce yarn with desired tenacity. the artificial neural network is used as a suitable structure for tenacity modeling of cotton yarn with 30 ne. as the first step for modeling, the empirical data is col...

Yarn tenacity is one of the most important properties in yarn production. This paper addresses modeling of yarn tenacity as well as optimally determining the amounts of the effective inputs to produce yarn with desired tenacity. The artificial neural network is used as a suitable structure for tenacity modeling of cotton yarn with 30 Ne. As the first step for modeling, the empirical data is col...

The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...

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 vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.