Abstract
Role of networks in our daily lives is very important. Effectiveness of network decreases with the breaking down of some nodes or links. So, less vulnerable communication network is required for greater stability. Vulnerability is the measure of the resistance of the network after failure of communication links. In this article, a graph has been considered for modeling a network and integrity as the measure of vulnerability, and the aim is to construct a graphic integer sequence of a graph or network with maximum number of edges from a given vertex order or number of vertices and graph integrity in linear time. Experiments show some possible graphs with maximum number of edges which obeys the given vertex order and integrity.
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