| Title: | Contributions to the Study of Contemporary Domination Invariants of Graphs |
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| Authors: | ID Brešar, Boštjan (Mentor) More about this mentor... 
ID Dravec, Tanja (Comentor) |
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| Files: |  DOK_Kos_Tim_2019.pdf (764,69 KB)
MD5: 2B0A1F010096A2C1B1B2383B026A1C46
PID: 20.500.12556/dkum/be3e1430-4ab2-45c4-a065-2533abde3ad3
 DOK_Kos_Tim_2019.zip (324,03 KB)
MD5: F27540FF7A8090988F77413EED7FB6CC
PID: 20.500.12556/dkum/90b8ad16-29fd-4b7d-a2d6-9c482c30d7ad
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| Language: | English |
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| Work type: | Doctoral dissertation |
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| Typology: | 2.08 - Doctoral Dissertation |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | This doctoral dissertation is devoted to contemporary domination concepts, such as the Grundy domination, the convex domination, the isometric domination and the total domination. Our main focus is to study their structure and algorithmic properties. Four Grundy domination invariants are presented, namely the Grundy domination number, the Grundy total domination number, the Z-Grundy domination number, and the L-Grundy domination number. Some bounds and properties of Grundy domination invariants are proven. All four Grundy domination parameters are studied on trees, bipartite distance-hereditary graphs, split graphs, interval graphs, Sierpi\'nski graphs, Kneser graphs and $P_4$-tidy graphs. Graphs with equal total domination number and Grundy total domination number are investigated.
Convex domination and isometric domination are studied on (weak) dominating pair graphs. For the chordal dominating pair graphs we present a polynomial algorithm to compute the convex domination number, and prove the NP-completeness of the corresponding decision problem for the chordal weak dominating pair graphs. For the isometric domination number of weak dominating pair graphs an efficient algorithm is presented.
Total domination is studied on the Cartesian product of graphs. We dedicate ourselves to graphs for which the equality holds in Ho's theorem, which states that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. |
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| Keywords: | Grundy domination, Grundy total domination, Z-Grundy domination, L-Grundy domination, convex domination, isometric domination, total domination, trees, split graphs, interval graphs, Sierpi\'nski graphs, Kneser graphs, modular decomposition, dominating pair graphs, Cartesian product |
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| Place of publishing: | [Maribor |
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| Publisher: | T. Kos] |
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| Year of publishing: | 2019 |
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| PID: | 20.500.12556/DKUM-73378 |
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| UDC: | 519.17(043.3) |
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| COBISS.SI-ID: | 302222080 |
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| NUK URN: | URN:SI:UM:DK:W7R53FG8 |
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| Publication date in DKUM: | 23.10.2019 |
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| Views: | 1761 |
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| Downloads: | 72 |
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| Metadata: |    |
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| Categories: | FNM
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