Invariance in divisor cordial labeling

Abstract

Divisor cordial labeling, Square divisor cordial labeling, Subtract divisor cordial labeling, Multiply divisor cordial labeling, Ring sum of graphs, Integer cordial labeling. newlineAim: Indicative aim of this research work is to verify particular existing graph labeling techniques and then to derive various new family of graphs which admit necessary condition(s) for particular labeling. The study revealed that not all graphs and graph families adhered to the condition of Divisor Cordial Labeling. Further, node and edge labeling technique was used to check the applicability of Divisor Cordial Labeling. In the end, all labeling patterns on various graphs along with their respective functions were defined under hypothetical conditions which is one of the prime goal of this research. newlineResults and Discussion: The present thesis is prepared to analyse mainly Divisor cordial labeling, Square divisor cordial labeling, Subtract divisor cordial labeling, Multiply divisor cordial labeling and Multiply divisor cordial labeling in context of ring sum of graphs. Some new families of graphs have been derived for these entire divisor cordial labeling. Results of multiply divisor cordial labeling are extended by using ring sum of two graphs. All the results in this research are mainly admitting divisor cordial labeling. The researcher s study facilitated construction of 36 new graphs admitting divisor cordial labeling by optimizing the applicability of graph theory and graph labeling. newlineConclusions: After analysis of all necessary condition(s) for labeling of a particular graph or family of graphs the considered graphs have been derived accordingly. From the study we can conclude that the divisor cordial labeling is a variant of cordial labeling as it fulfils all the prerequisite conditions. newline