Document Details

Document Type : Thesis 
Document Title :
STUDIES ON SOME GRAPHS
دراسة على بعض الرواسم
 
Subject : Faculty of Sciences 
Document Language : Arabic 
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. 
Supervisor : Prof. Ahmad Nasser AL-Kenani 
Thesis Type : Doctorate Thesis 
Publishing Year : 1439 AH
2017 AD 
Added Date : Sunday, October 22, 2017 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عمر عبدالرحمن العطاسAl-Attas, Omar AbdulrahmanResearcherDoctorate 

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