The median function on graphs with bounded profiles Original Research Article

The median of a profile image of vertices of a graph image is the set of vertices image that minimize the sum of distances from image to the vertices of image. It is shown that for profiles image with diameter image the median set can be computed within an isometric subgraph of image that contains a vertex image of image and the image-ball around image, where image. The median index of a graph and image-joins of graphs are introduced and it is shown that image-joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.