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Title: A study of inverse, mixed block domination and related concepts in graphs
Researcher: Surekha
Guide(s): Bhat, Pradeep G
Keywords: Mathematics
mixed block domination
Upload Date: 25-Oct-2013
University: Manipal University
Completed Date: 27/09/2013
Abstract: It is proved that every graph is a block tree. Varieties of block- degrees and block-regular graphs have been defined. Expressions for the sum of block degrees are obtained. Several bounds for number of blocks and number of cutvertices in a graph are obtained. Using block distance we defined the central tendencies of a block, like B-radius and B-diameter of a graph. It is proved that block center of any graph is B-complete. Expressions for number of edges in the newly defined graphs are derived. Various block domination parameters are defined. A vertex vand#61646;V and a block band#61646;B (G) is said to block dominate (b-dominate) each other if v is incident on the block b. A set D and#61645; V is said to be a vertex-block dominating set (VBD set) if every block in G is b-dominated by some vertex in D. The vertex - block domination number and#61543;vb = and#61543;vb(G) is the cardinality of a minimum block dominating set of G. We initiate a study of these new varieties of mixed block domination in graphs. We define another parameter called inverse independence number of a graph. Extending the same concept for edge independent sets inverse matching number of a graph is defined. Using minimum clique number , independent domination number of complement of any graph G is obtained. Finally in the last section, various inverse block domination parameters are defined and initiated the study of properties of inverse block domination.
Pagination: 101p.
Appears in Departments:Manipal Institute of Technology

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02_certificate.pdf146.51 kBAdobe PDFView/Open
03_abstract.pdf201.14 kBAdobe PDFView/Open
04_declaration.pdf141.82 kBAdobe PDFView/Open
05_acknowledgements.pdf394.65 kBAdobe PDFView/Open
06_contents.pdf586.05 kBAdobe PDFView/Open
07_list of tables.pdf330.69 kBAdobe PDFView/Open
08_list of figures.pdf126.91 kBAdobe PDFView/Open
09_chapter 1.pdf988.95 kBAdobe PDFView/Open
10_chapter 2.pdf908.99 kBAdobe PDFView/Open
11_chapter 3.pdf544.08 kBAdobe PDFView/Open
12_chapter 4.pdf916.6 kBAdobe PDFView/Open
13_chapter 5.pdf714.38 kBAdobe PDFView/Open
14_chapter 6.pdf708.27 kBAdobe PDFView/Open
15_conclusion.pdf301 kBAdobe PDFView/Open
16-bibliography.pdf189.86 kBAdobe PDFView/Open

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