A single assignment of numbers for square divisor cordial and cube divisor cordial labelings on the generalized Petersen graphs GP (n,3)

Abstract

In this paper, a work on the generalized Petersen graph GP [Formula: see text] is done, proving Generalized Petersen graph GP [Formula: see text] to be both Square Divisor Cordial Graphs and Cube Divisor Cordial Graphs by a single assignment of numbers on the same graph. Few conditions are provided to label the graphs in single assignment to prove two different labelings. A rule is developed to label the graphs and the results obtained are tabulated by actual verification for [Formula: see text] to [Formula: see text] but the rule holds good for all [Formula: see text] 4. Further, a few illustrations are provided to justify the rule given to label the graphs in a single assignment.