| Title: | Partitioning the vertex set of ▫$G$▫ to make ▫$G \Box H$▫ an efficient open domination graph |
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| Authors: | ID Kraner Šumenjak, Tadeja (Author)
ID Peterin, Iztok (Author)
ID Rall, Douglas F. (Author)
ID Tepeh, Aleksandra (Author) |
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| Files: |  Discrete_Mathematics_&_Theoretical_Computer_Science_2016_Kraner_Sumenjak_et_al._Partitioning_the_vertex_set_of_G_to_make_GBoxH_an_effici.pdf (166,60 KB)
MD5: 20EB038F9F8D9EBB93887CF7B8EC698F
PID: 20.500.12556/dkum/ef6db32f-efb1-4e21-b2c1-74faf2d1a55f
 http://dmtcs.episciences.org/1503
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FKBV - Faculty of Agriculture and Life Sciences
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| Abstract: | A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs ▫$G$▫ for which the Cartesian product ▫$G \Box H$▫ is an efficient open domination graph when ▫$H$▫ is a complete graph of order at least 3 or a complete bipartite graph. The characterization is based on the existence of a certain type of weak partition of ▫$V(G)$▫. For the class of trees when ▫$H$▫ is complete of order at least 3, the characterization is constructive. In addition, a special type of efficient open domination graph is characterized among Cartesian products ▫$G \Box H$▫ when ▫$H$▫ is a 5-cycle or a 4-cycle. |
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| Keywords: | efficient open domination, Cartesian product, vertex labeling, total domination |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2016 |
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| Number of pages: | str. 1-15 |
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| Numbering: | Letn. 18, št. 3 |
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| PID: | 20.500.12556/DKUM-66784  |
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| ISSN: | 1365-8050 |
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| UDC: | 519.17:004 |
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| ISSN on article: | 1365-8050 |
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| COBISS.SI-ID: | 17696601 |
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| NUK URN: | URN:SI:UM:DK:KGS5WHX1 |
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| Publication date in DKUM: | 10.07.2017 |
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| Views: | 1228 |
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| Downloads: | 186 |
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| Metadata: |    |
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| Categories: | Misc.
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