Bibliographic Details
| Title: |
An extension of locating-total domination problem and its complexity. |
| Authors: |
Eswar, N.1 (AUTHOR) jgopal89@gmail.com, Jayagopal, R.1 (AUTHOR) jgopal89@gmail.com |
| Source: |
RAIRO: Operations Research (2804-7303). 2024, Vol. 58 Issue 6, p4889-4904. 16p. |
| Subjects: |
NP-complete problems, Necklaces, Silicates, Dominating set |
| Abstract: |
An r-dominating set (r-total dominating set) of G is a subset S of V (G) for which Nr(u)∩S is non-empty for all u not in S (for all u in V (G)). An r-locating-dominating set (r-locating-total dominating set) of G is an r-dominating set (r-total dominating set) S of G for which Nr(u) ∩S is different from Nr(v) ∩S for all u and v not in S. This paper presents an extension of the locating-total dominating set of G. Further, we establish a lower bound on r-locating-dominating set and r-locating-total dominating set for k-regular graphs, as well as demonstrate that r-locating-total dominating set is an NP-complete problem. Furthermore, the r-locating-dominating set and r-locating-total dominating set problems are discussed for some standard graphs. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
