Name
Abstract | ||
|---|---|---|
Let S be a primitive non-powerful signed digraph of order n. The base of a vertex it, denoted by l(S)(u), is the smallest positive integer I such that there is a pair of SSSD walks of length t from it to each vertex upsilon is an element of V(S) for any integer t >= l. We choose to order the vertices of S in such a way that l(S)(1) <= l(S)(2) <= l(S)(n) and call l(S)(k) the kth local bast, of S for 1 <= k <= n. In this work, we use PNSSD to denote the class of all primitive non-powerful signed symmetric digraphs of order n with at least one loop. Let l(k) be the largest value of l(S)(k) for S is an element of PNSSD, and L(k) = {l(S)(k) vertical bar S is an element of PNSSD). For n >= 1 and 1 < k < n - 1, we show l(S)(k) = 2n - 1 and L(k) {2, 3, ..., 2n-1}. Further, we characterize all primitive non-powerful signed symmetric digraphs whose kth local bases attain l(k). |
Year | DOI | Venue |
|---|---|---|
2009 | null | ARS COMBINATORIA |
Keywords | Field | DocType |
Signed digraph,Primitive digraph,Local base | Discrete mathematics,Combinatorics,Mathematics | Journal |
Volume | Issue | ISSN |
90 | null | 0381-7032 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yanling Shao | 1 | 4 | 4.96 |
| Yu-Bin Gao | 2 | 6 | 7.70 |