Name
Abstract | ||
|---|---|---|
digraph D with p vertices and q arcs is labeled by assigning a distinct integer value g ( v ) from {0,1, , q } to each vertex v . The vertex values, in turn, induce a value g ( u, v ) on each arc ( u, v ) where g ( u, v ) = ( g ( v ) g ( u ))( mod q + 1). If the arc values are all distinct then the labeling is called a graceful labeling of a digraph. Bloom and Hsu (SIAM J Alg Discr Methods 6:519---536, 1985 ) conjectured that, all unicyclic wheels are graceful. Also, Zhao et al. (J Prime Res Math 4:118---126, 2008 ) conjectured that, for any positive even n and any integer m 14, the digraph $${n-\overrightarrow{C_m}}$$ is graceful. In this paper, we prove both the conjectures. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s00373-012-1159-x | Graphs and Combinatorics |
Keywords | Field | DocType |
generating functions,graceful digraphs,partitions,unicyclic wheels | Prime (order theory),Integer,Generating function,Discrete mathematics,Combinatorics,Vertex (geometry),Graceful labeling,Mathematics,Digraph | Journal |
Volume | Issue | ISSN |
29 | 4 | 1435-5914 |
Citations | PageRank | References |
1 | 0.48 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. M. Hegde | 1 | 32 | 9.96 |
| Shivarajkumar | 2 | 1 | 0.82 |