Name
Abstract | ||
|---|---|---|
A perfect code in a graph =(V,E) is a subset C of V that is an independent set such that every vertex in VC is adjacent to exactly one vertex in C. A total perfect code in is a subset C of V such that every vertex of V is adjacent to exactly one vertex in C. A perfect code in the Hamming graph H(n,q) agrees with a q-ary perfect 1-code of length n in the classical setting. In this paper we give a necessary and sufficient condition for a circulant graph of degree p1 to admit a perfect code, where p is an odd prime. We also obtain a necessary and sufficient condition for a circulant graph of order n and degree pl1 to have a perfect code, where p is a prime and pl the largest power of p dividing n. Similar results for total perfect codes are also obtained in the paper. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.disc.2017.02.007 | Discrete Mathematics |
Keywords | Field | DocType |
Perfect code,Total perfect code,Efficient dominating set,Efficient open dominating set,Cayley graph,Circulant graph | Perfect graph,Discrete mathematics,Combinatorics,Circulant graph,Vertex (graph theory),Perfect power,Neighbourhood (graph theory),Regular graph,Trivially perfect graph,Mathematics,Perfect graph theorem | Journal |
Volume | Issue | ISSN |
340 | 7 | Discrete Mathematics 340 (2017) 1522-1527 |
Citations | PageRank | References |
4 | 0.45 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rongquan Feng | 1 | 117 | 25.64 |
| He Huang | 2 | 79 | 18.92 |
| Sanming Zhou | 3 | 80 | 12.48 |