The Average Lower Connectivity of Graphs

Abstract

For a vertexvof a graphG, thelower connectivity, denoted bysv(G), is the smallest number of vertices that containsvand those vertices whose deletion fromGproduces a disconnected or a trivial graph. The average lower connectivity denoted byκav(G)is the value(∑v∈VGsvG)/VG. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs.