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

Abstract

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