Role of Graphic Integer Sequence in the Determination of Graph Integrity

Debajit Sensarma and Samar Sen Sarma
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Debajit Sensarma: Department of Computer Science, Vivekananda Mission Mahavidyalaya, Chaitanyapur (Haldia), Purba Medinipur 721645, India
Samar Sen Sarma: Department of Computer Science & Engineering, University of Calcutta Kolkata, Kolkata 700073, India

Mathematics, 2019, vol. 7, issue 3, 1-12

Abstract: Networks have an important role in our daily lives. The effectiveness of the network decreases with the breaking down of some vertices or links. Therefore, a less vulnerable communication network is required for greater stability. Vulnerability is the measure of resistance of the network after failure of communication links. In this article, a graph has been taken for modeling a network and integrity as a measure of vulnerability. The approach is to estimate the integrity or upper bound of integrity of at least one connected graph or network constructed from the given graphic integer sequence. Experiments have been done with random graphs, complex networks and also a comparison between two parameters, namely the vertex connectivity and graph integrity as a measure of the network vulnerability have been carried out by removing vertices randomly from various complex networks. A comparison with the existing method shows that the algorithm proposed in this article provides a much better integrity measurement.

Keywords: vulnerability; graphic integer sequence; integrity; tenacity; rupture degree; scattering number; independence number; covering number; clique number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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