EQUITABLE COLORING IN PATH, CYCLE, AND RELATED GRAPH CLASSES UNDER Gxyz OPERATIONS

Abstract

Our research focuses on determining the equitable chromatic number associated with a defined operation , where , applied to a variety of graph classes. Specifically, we analyze the behavior of this parameter across path, cycle, wheel, umbrella, tadpole, sundat, and octopus graphs. Our results provide insights into the structural implications of the  transformation on equitable coloring properties within these graph families.