Component Edge Connectivity and Extra Edge Connectivity of Bubble-Sort Star Graphs

Abstract

Connectivity is an important parameter for evaluating the reliability and stability of an interconnection network. Based on the edge connectivity, more refined connectivities have been proposed. The [Formula: see text]-component edge connectivity [Formula: see text] and the [Formula: see text]-extra edge connectivity [Formula: see text] are two important parameters to assess the robustness of an interconnection network, which received attention extensively. In this paper, we determine the [Formula: see text]-component edge connectivity and the [Formula: see text]-extra edge connectivity of bubble-sort star graphs [Formula: see text]. For [Formula: see text]-component edge connectivity, we prove that [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text]. For [Formula: see text]-extra edge connectivity, we prove that [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text].