A note on locating a central vertex of a 3-cactus graph

The authors extend linear time algorithms for a variety of vertex location measures on trees to include 3-cactus graphs. To do this the original 3-cactus graph is transformed into a tree. The behavior of median and variance measures under this transformation is studied and linear (in the number of vertices) time complexity algorithms for the minimum weighted vertex variance problem and the vertex restricted stochastic queue median are developed.