in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system’s high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. In this paper, we show that the largest connected component of the survival graph contains almost all...

The systematic protection of critical information infrastructures requires an analytical process to identify the critical components and their interplay, to determine the threats and vulnerabilities, to assess the risks and to prioritise countermeasures where risk is unacceptable. This paper presents an integrated framework for model-based symbolic interpretation, simulation and analysis with a...

In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop redundancy) and system resilience, viewed as the antonym to structural vulnerability, are assessed. Deterministic techniques from complex networks and spectral grap...

This study aimed to investigate the influence of apolipoprotein E (APOE) ε4 allele on whole-brain functional networks in cognitively normal (CN) elderly by applying graph theoretical analysis to brain glucose metabolism. Eighty-six CN elderly [28 APOE ε4 carriers (ε4+) and 58 non-carriers (ε4-)] underwent clinical evaluation and resting [(18)F] fluorodeoxyglucose positron emission tomography sc...

Effective management of infrastructural networks in the case of a crisis requires a prior analysis of the vulnerability of spatial networks and identification of critical locations where an interdiction would cause most damage and disruption. This paper presents a preliminary study into how a graph theoretic structural analysis could be used for this purpose. Centrality measures are combined wi...

A Continuous Monitoring System (CMS) model is presented, having new improved capabilities. The system is based on the actual real-time configuration of the system. Existing risk scoring models assume damage potential is estimated by systems' owner, thus rejecting the information relying in the technological configuration. The assumption underlying this research is based on users' ability to est...

a r t i c l e i n f o a b s t r a c t Fault tolerance is especially important for interconnection networks, since the growing size of the networks increases its vulnerability to component failures. A classic measure for the fault tolerance of a network in the case of vertex failures is its connectivity. Given a network based on a graph G and a positive integer h, the R h-connectivity of G is th...

One of the most important research topics about complex networks
 is examination their vulnerability. Therefore, there are many studies
 in literature analyzing robustness and reliability using graph theoretical parameters. Among these parameters, centrality
 parameters play an role.The closeness its derivatives
 widely discussed. In this study, parameter more sensitive&#x0D...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...