Name
Abstract | ||
|---|---|---|
Identifying and locating-dominating codes have been studied widely in circulant graphs of type \(C_{n}(1,2,3,\dots , r)\) over the recent years. In 2013, Ghebleh and Niepel studied locating-dominating and identifying codes in the circulant graphs \(C_{n}(1,d)\) for \(d = 3\) and proposed as an open question the case of \(d > 3\). In this paper we study identifying, locating-dominating and self-identifying codes in the graphs \(C_{n}(1,d)\), \(C_{n}(1,d-1,d)\) and \(C_{n}(1,d-1,d,d + 1)\). We give a new method to study lower bounds for these three codes in the circulant graphs using suitable grids. Moreover, we show that these bounds are attained for infinitely many parameters n and d. In addition, new approaches are provided which give the exact values for the optimal self-identifying codes in \(C_{n}(1,3)\) and \(C_{n}(1,4)\). |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s12095-018-0316-3 | Cryptography and Communications |
Keywords | Field | DocType |
Identifying code, Locating-dominating code, Circulant graph, Square grid, Triangular grid, King grid, 94B25, 94B65, 05C69, 05B40 | Discrete mathematics,Graph,Combinatorics,Circulant matrix,Mathematics | Journal |
Volume | Issue | ISSN |
abs/1802.01325 | 4 | 1936-2447 |
Citations | PageRank | References |
1 | 0.37 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ville Junnila | 1 | 43 | 10.51 |
| Tero Laihonen | 2 | 363 | 39.39 |
| Gabrielle Paris | 3 | 1 | 0.37 |