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...

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...

the tenacity of a graph g, t(g), is de ned by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we de ne τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

In 1962, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d1, d2, . . . , dn to be the degree sequence of a non–separable graph or that of a connected graph. Our goal in this note is to utilize these results to prove closed formulas for the functions dns(2m) and dc(2m), the number of degree sequences with degree sum 2m representable by non–separa...

Introduction: Long-term stressful situations can drastically influence one’s mental life. However, the effect of mental stress on recognition of emotional stimuli needs to be explored. In this study, recognition of emotional stimuli in a stressful situation was investigated. Four emotional conditions, including positive and negative states in both low and high levels of arousal were analy...

The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...

Measures of network structural integrity useful in the analysis and synthesis of power systems are discussed. Signal flow methodology is applied to derive an expression for the paths between sources and sinks in a power network. Connectivity and reach ability properties of the network are obtained using the minors of a modified connectivity matrix. Node-connectivity, branch connectivity and mix...

We study a directed network design problem called the k-(S, T )-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer k, the minimum cost k-vertex connected spanning subgraph problem is a special case of the k(S, T )-connectivity problem. We defer precise statements of the problem and of our results to the introduction. For k =...