| Autor: |
Huaming Xing, Moo Young Sohn |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Information Processing Letters. 115:950-956 |
| ISSN: |
0020-0190 |
| Popis: |
The problem of placing monitoring devices in a system in such a way that every site in the safeguard system (including the monitors themselves) is adjacent to a monitor site can be modeled by total domination in graphs. Locating-total dominating sets are of interest when the intruder/fault at a vertex precludes its detection in that location. A total dominating set S of a graph G with no isolated vertex is a locating-total dominating set of G if for every pair of distinct vertices u and v in V - S are totally dominated by distinct subsets of the total dominating set. The locating-total domination number of a graph G is the minimum cardinality of a locating-total dominating set of G. In this paper, we study the bounds on locating-total domination numbers of the Cartesian product C m ? P n of cycles C m and paths P n . Exact values for the locating-total domination number of the Cartesian product C 3 ? P n are found, and it is shown that for the locating-total domination number of the Cartesian product C 4 ? P n this number is between ? 3 n 2 ? and ? 3 n 2 ? + 1 with two sharp bounds. We show that the locating-total domination number of the Cartesian product C 3 ? P n is equal to n + 1 .We show that for the locating-total domination number of the Cartesian product C 4 ? P n this number is between ? 3 n 2 ? and ? 3 n 2 ? + 1 with two sharp bounds. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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