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- W3134875537 abstract "Graph has seen an explosive growth due to interaction with areas like computer science, electrical and communication engineering, operations research etc. In this thesis, we are interested in the domination and the energy of graphs which are the most important in the theory of graphs. First, we introduce a new graph called near common-neighborhood graph of a graph, we study some basic properties and results of this graph and obtain a new formula for its adjacency matrix. The new definition motivated us to make characterization for the graphs by defining the near common neighborhood graph. Furthermore, by studying the iterated of the near common neighborhood graph of a graph we define new invariant called near-common neighborhood completeness number of a graph. One focus of this thesis is on the domination of graphs, we introduce a new domination parameter called co-common neighborhood domination and find out the exact values of some families of graphs, some relations with the other domination parameters are established. We also define CCN-independence number, total CCN-domination number, CCN-covering number and CCN-domatic number. Finally, we introduce a new type of graph energy called the non-common neighborhood energy E_NCN (G), NCN-energy for some standard graphs is obtained and an upper bound for E_NCN (G) is found when G is a strongly regular graph. Also the relation between common neighborhood energy and non-common neighborhood energy of a graph is established." @default.
- W3134875537 created "2021-03-15" @default.
- W3134875537 creator A5071832513 @default.
- W3134875537 date "2017-01-01" @default.
- W3134875537 modified "2023-09-26" @default.
- W3134875537 title "STUDIES ON SOME GRAPHS" @default.
- W3134875537 hasPublicationYear "2017" @default.
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