Title
Automorphic Decompositions of Graphs
Document Type
Article
Publication Date
3-1-2011
Description
A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. The intersection graph I (D)of the decomposition D has a vertex for each part of the partition and two parts A and B are adjacent iff they share a common node in H. If I (D) ≅ H, then D is an automorphic decomposition of H. In this paper we show how automorphic decompositions serve as a common generalization of configurations from geometry and graceful labelings on graphs. We will give several examples of automorphic decompositions as well as necessary conditions for their existence.
Citation Information
Beeler, Robert A.; and Jamison, Robert E.. 2011. Automorphic Decompositions of Graphs. Graphs and Combinatorics. Vol.27(2). 149-160. https://doi.org/10.1007/s00373-010-0981-2 ISSN: 0911-0119