Decomposition of Graphs and Labeling Techniques

Abstract

The decomposition of graphs is one of the potential areas of research in mathematics due to its vital applications in networking, block design and bioinformatics. newlineThe problems related to labeling of graphs challenge human mind for their eventual solutions. The concept of decomposition of graphs and labeling of graphs were introduced by Alexander Rosa in 1960. Various graph labeling techniques and graph decompositions are available now, and more than two thousand research papers have been published so far in these areas. H and#8722; magic decomposition of graphs arises from the combination of graph labeling and graph decomposition. In this thesis, it is the keystone which with different attributes in the field of H and#8722; magic decomposition of graphs. newlineThe primary objective of this research is to examine the different types of decomposition of graphs with labeling techniques such as star vertex super magic decomposition of graphs, cycle vertex super magic decomposition of graphs and C4and#8722;vertex super magic decomposition of graphs. The minimum and maximum magic constant are examined for various star vertex super magic decomposition of graphs. newlineAn earnest attempt has been made through this thesis to contribute substantially towards the investigation of the new concept H and#8722; vertex super bimagic decomposition of graphs. newlineThe secondary focus of the research is to examine the Hamiltonand#8722;edge super magic decomposition of graphs and then investigate the 2and#8722; factor edge super bimagic decomposition of graphs. Moreover, the H and#8722; totally magic cordial decomposition of graphs is introduced exploring its magic constant. newlineThe next focus of the research work is to obtain the geometric decomposition of several graphs with variations in first term and common ratio. newline newline