Further study on k-restricted edge connectivity and exact k-restricted edge connectivity of a graph.

Inspired by the studies on conditional connectivity by Harary [1], we worked on k-restricted edge connectivity of a graph G [4]. The k-restricted edge connectivity of a graph G is the cardinality of a minimum edge-cut whose deletion disconnects the graph G into components where each component has order at least k. In this work, we take into account some results on k-restricted edge connectivity and the novel parameter exact k-restricted edge connectivity. In the definition of k-restricted edge connectivity, we impose some extra constraints to achieve this parameter. In this paper, we consider some fundamental aspects of exact k-restricted edge connectivity and how they relate to the k-restricted edge connectivity. [ABSTRACT FROM AUTHOR]