What are the different proximity functions or distance metrics used for the K-means algorithm?

Euclidean, Manhattan, Cosine, and Bregman divergence are some distance metrics used for the K-means algorithm. Euclidean is the squared distance from a data point to the centroid. Manhattan is the absolute distance from a data point to the centroid. Cosine is the cosine distance from a data point to the cluster centroid. Bregman divergence is a class of distance metrics that includes Euclidean, Mahalanobis, and Cosine. Basically, Bregman divergence includes all those distance metrics for which the mean is a centroid.