Malota, RidsonRidsonMalota2025-02-062025-02-062021-08-01https://dspace.unima.ac.mw/handle/123456789/768Submitted to the Department of Mathematical Sciences, Faculty of Science, in partial fulfillment of the requirements for the degree of Master of Science (Mathematical Sciences)The measures of global connectivity such as graph integrity and toughness have non-polynomial time complexities. This has led to the development of global average graph vertex connectivity measures that are dependent on combinatoric counting of number of internally disjoint paths in a graph. Many results related to average vertex connectivity have been found. This study develops a spectral form of average vertex connectivity, together with its upper bounds. Using trees, we demonstrate that the new definition and its upper bounds are more related to ordinary graph parameters.enGraphVertex connectivityNon- polynomialGlobal connectivityGraph integrityNon-polynomial time complexitiesAverage vertex connectivitytext::thesis::master thesis