| Title:
|
Exact $2$-step domination in graphs (English) |
| Author:
|
Chartrand, Gary |
| Author:
|
Harary, Frank |
| Author:
|
Hossain, Moazzem |
| Author:
|
Schultz, Kelly |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
125-134 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a vertex $v$ in a graph $G$, the set $N_2(v)$ consists of those vertices of $G$ whose distance from $v$ is 2. If a graph $G$ contains a set $S$ of vertices such that the sets $N_2(v)$, $v\in S$, form a partition of $V(G)$, then $G$ is called a $2$-step domination graph. We describe $2$-step domination graphs possessing some prescribed property. In addition, all $2$-step domination paths and cycles are determined. (English) |
| Keyword:
|
$2$-step domination graph |
| Keyword:
|
paths |
| Keyword:
|
cycles |
| MSC:
|
05C12 |
| MSC:
|
05C38 |
| MSC:
|
05C70 |
| idZBL:
|
Zbl 0863.05050 |
| idMR:
|
MR1357597 |
| DOI:
|
10.21136/MB.1995.126228 |
| . |
| Date available:
|
2009-09-24T21:09:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126228 |
| . |
| Reference:
|
[1] G. Chartrand, L. Lesniak: Graphs & Digraphs.(second edition). Wadsworth k. Brooks/Cole, Monterey, 1986. Zbl 0666.05001, MR 0834583 |
| Reference:
|
[2] F. Harary: Graph Theory.Addison-Wesley, Reading, 1969. Zbl 0196.27202, MR 0256911 |
| . |
