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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-17738 |
| Date | 01 March 2011 |
| Creators | Beeler, Robert A., Jamison, Robert E. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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