Study on Graceful Labeling

Abstract

ABSTRACT newlineThe labeling of graphs is one of the potential areas of research due to its vital newlineapplications. The problems related to labeling of graphs challenge our mind for their newlineeventual solutions. The concept of graph labeling was introduced by Alexander Rosa newlinein mid-sixties. Various graph labeling techniques are available now and above two newlinethousand research papers have been published so far in this area. newlineThe primary objective of this research is to examine odd graceful labeling newlineand even graceful labeling. An earnest attempt has been made through this thesis to newlinecontribute substantially towards the investigation of the new concept, even-even newlinegraceful labeling and exploring its labeling techniques. The secondary focus of the newlineresearch is to analyze the relation between different types of graceful labeling newlinenamely odd-even graceful labeling and even graceful labeling. Then, investigate the newlinerelation between graceful labeling with signed product cordial labeling and the relation newlinebetween even graceful graph and (n + k) -equitable graph * newlinen+k P . Moreover, the newlinerelation between even-even graceful labeling and other labeling such as E-cordial newlinelabeling, totally magic cordial labeling, multiplicative labeling, multiplicative divisor newlinelabeling and strongly multiplicative labeling are investigated. Also, the concept of newlinecomplementary edge-odd graceful labeling is introduced. newlineThe major contribution made in this thesis is the introduction of the eveneven newlinegraceful labeling and k -even-even edge graceful labeling. Many variations and newlinegeneralizations of labeling of graphs have been studied by many authors in many newlineways. Graceful labeling of graphs has found a lot of applications. In this thesis an newlineoutline of one of the uses of the new k -even-even edge graceful labeling in the newlineMPLS network is provided. Here, the new k -even-even edge graceful theorem has newlinebeen used to create a unique label or identifier to each IP network destination. This is newlineachievable only by assigning labels to every destination networks and forwarding the newlinetraffic bas