The Shields–Harary numbers of image for continuous concave cost functions vanishing at 1

It is shown that the Shields–Harary index of vulnerability of the complete bipartite graph image, with respect to the cost function image, image, is m, if image, and image, if image. It follows that the Shields–Harary number of image with respect to any concave continuous cost function f on image satisfying image is image, if image, and between image and image, if image.