Abstract: Let be a graph on n vertices and C a collection of n subgraphs of H, one for each vertex. Then C is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of C and any two members of C share a unique edge whenever the corresponding vertices are adjacent in H. If all subgraphs in C are isomorphic to a given graph , then C is said to be an ODC of H by G. We construct ODCs of H by the union of a path and a star, where the center of the star is one of the path end-vertices, for M=5,6,7,8,9,10). All these ODCs are generated by symmetric starters with respect to the cyclic group of order n.
A note on orthogonal double covers of complete bipartite graphs by a special class of six caterpillars.
SCAPELLATO, RAFFAELE
2010-01-01
Abstract
Abstract: Let be a graph on n vertices and C a collection of n subgraphs of H, one for each vertex. Then C is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of C and any two members of C share a unique edge whenever the corresponding vertices are adjacent in H. If all subgraphs in C are isomorphic to a given graph , then C is said to be an ODC of H by G. We construct ODCs of H by the union of a path and a star, where the center of the star is one of the path end-vertices, for M=5,6,7,8,9,10). All these ODCs are generated by symmetric starters with respect to the cyclic group of order n.| File | Dimensione | Formato | |
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