Minimal doubly resolving sets and the strong metric dimension of Hamming graphs
2012
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We consider the problem of determining the cardinality Ψ (H2,k) of minimal doubly resolving sets of Hamming graphs H2,k.We prove that for k ≥ 6 every minimal resolving set of H2,k is also a doubly resolving set, and, consequently, Ψ (H2,k) is equal to the metric dimension of H2,k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs Hn,k.
Ključne reči:
strong metric dimension / minimal doubly resolving set / metric dimension / Hamming graphs / graph theoryIzvor:
Applicable Analysis and Discrete Mathematics, 2012, 6, 1, 63-71Izdavač:
- Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
Finansiranje / projekti:
- Teorija grafova i matematičko programiranje sa primenama u hemiji i računarstvu (RS-MESTD-Basic Research (BR or ON)-174033)
DOI: 10.2298/AADM111116023K
ISSN: 1452-8630
WoS: 000302764100004
Scopus: 2-s2.0-84867975574
Institucija/grupa
Fakultet organizacionih naukaTY - JOUR AU - Kratica, Jozef AU - Kovačević-Vujčić, Vera AU - Čangalović, Mirjana AU - Stojanović, Milica PY - 2012 UR - https://rfos.fon.bg.ac.rs/handle/123456789/930 AB - We consider the problem of determining the cardinality Ψ (H2,k) of minimal doubly resolving sets of Hamming graphs H2,k.We prove that for k ≥ 6 every minimal resolving set of H2,k is also a doubly resolving set, and, consequently, Ψ (H2,k) is equal to the metric dimension of H2,k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs Hn,k. PB - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd T2 - Applicable Analysis and Discrete Mathematics T1 - Minimal doubly resolving sets and the strong metric dimension of Hamming graphs EP - 71 IS - 1 SP - 63 VL - 6 DO - 10.2298/AADM111116023K UR - conv_1030 ER -
@article{ author = "Kratica, Jozef and Kovačević-Vujčić, Vera and Čangalović, Mirjana and Stojanović, Milica", year = "2012", abstract = "We consider the problem of determining the cardinality Ψ (H2,k) of minimal doubly resolving sets of Hamming graphs H2,k.We prove that for k ≥ 6 every minimal resolving set of H2,k is also a doubly resolving set, and, consequently, Ψ (H2,k) is equal to the metric dimension of H2,k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs Hn,k.", publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd", journal = "Applicable Analysis and Discrete Mathematics", title = "Minimal doubly resolving sets and the strong metric dimension of Hamming graphs", pages = "71-63", number = "1", volume = "6", doi = "10.2298/AADM111116023K", url = "conv_1030" }
Kratica, J., Kovačević-Vujčić, V., Čangalović, M.,& Stojanović, M.. (2012). Minimal doubly resolving sets and the strong metric dimension of Hamming graphs. in Applicable Analysis and Discrete Mathematics Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 6(1), 63-71. https://doi.org/10.2298/AADM111116023K conv_1030
Kratica J, Kovačević-Vujčić V, Čangalović M, Stojanović M. Minimal doubly resolving sets and the strong metric dimension of Hamming graphs. in Applicable Analysis and Discrete Mathematics. 2012;6(1):63-71. doi:10.2298/AADM111116023K conv_1030 .
Kratica, Jozef, Kovačević-Vujčić, Vera, Čangalović, Mirjana, Stojanović, Milica, "Minimal doubly resolving sets and the strong metric dimension of Hamming graphs" in Applicable Analysis and Discrete Mathematics, 6, no. 1 (2012):63-71, https://doi.org/10.2298/AADM111116023K ., conv_1030 .