A Study of Liouville Difference Cordial Labeling in Cyclic Graph Classes

Graph labeling plays a significant role in the study of graph structures and their interactions with number-theoretic concepts. Recently, Liouville Difference Cordial labeling was introduced by combining the Liouville function with difference cordial labeling and was shown to exist for several classes of acyclic graphs. In this paper, we extend the investigation of LDC labeling to cyclic graph classes. Specifically, we examine the existence of Liouville Difference Cordial labelings for cycle graphs, sun graphs, and Dutch windmill graphs. Suitable labeling constructions are provided, and it is established that these graph families admit LDC labelings under the proposed assignments. The results expand the class of graphs known to possess Liouville Difference Cordial labelings and demonstrate the applicability of the labeling scheme beyond acyclic structures. This work further strengthens the connection between graph labeling and number theory and opens new directions for the study of Liouville-based labelings on more complex graph families.