Study on graceful harmonious and cordial graphs

Abstract

Much interest in graph labelings began in mid 1960s with the conjecture of Ringel and a paper by Rosa The popular Ringel Kotzig conjecture that all trees are graceful remains unsettled In his classic paper Rosa introduced and#946;valuation and#945;valuation and other labelings as a tool to decompose complete graphs This labeling was later called graceful by Golomb and now this is the term most widely used Graham and Sloane introduced harmonious labeling in connection with their study on additive bases problem stemming from error correcting codes Over the period variations of graceful and harmonious labeling were studied with different motivations Chang introduced elegant labeling as a variation of harmonious labeling Cordial labeling was introduced by Cahit as a variation of both graceful and harmonious labeling Over the period of four decades the field of graph labeling has experienced rapid growth However the fundamental understanding that the characterization of graceful and other labeled graphs appears to be one of the most difficult and hard problems in graph theory