A Study on Cordial Labeling and Harmonious Labeling in Graph Theory

Abstract

In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers to edges and vertices of a graph. The basic graph labelings, graceful and harmonious labeling be defined. The separation of graceful and harmonious category namely, valuation, elegant labeling and cordial labeling are also definite. These labeling are used all over this thesis. Much interest in graph labelings began in mid 1960and#8223;s with the conjecture. The accept Ringel conjecture that all trees are graceful, excess unsettled. In his classic paper, Rosa introduced valuation and other labelings as a tool to decompose complete graphs. The evaluation was later called graceful labeling is the term most widely used. Graceful and harmonious labeling the two basic labeling was extensively studied. Variations of graceful and harmonious specifically, appraisal, elegant and cordial labeling have been introduced with different motivations in the field of graph labeling. Over the period of four decades, more than six hundred papers have explained on this topic. This proves the rapid growth of the field. However, the essential understanding that the description of graceful and previous labeled graph appears to be one of the mainly complex and strong trouble in graph theory. In fact, approval of the simplest labeled graph, namely cordial graph, is a NP-complete difficulty. The problems of these labelings, many mathematicians have exposed attention in if necessary circumstances and different enough conditions on labelled graphs hoping to progress the understanding of the attribute natural history of the labeled chart.