Balanced star decompositions of regular multigraphs and image-fold complete bipartite graphs Original Research Article

Let image denote the star with k edges. A balanced image-decomposition of a multigraph G is a family image of subgraphs of G whose edge sets form a partition of the edge set of G such that each member of image is isomorphic to image, and every vertex of G belongs to the same number of members in image. In this paper, we obtain the following results: (1) A necessary and sufficient condition for an r-regular multigraph to have a balanced image-decomposition. (2) A necessary and sufficient condition for the image-fold complete bipartite graph image to have a balanced image-decomposition.