On Divisor Cordial Labeling of Certain Classes of Planar Graphs

Abstract

A DCL of G(V, E) is defined by a bijection f : V  → {1, 2, ..., |V |} such that every line uv is given 1 if f (u)|f (v) or f (v)|f (u) and  0 otherwise; then the positive difference of the count of edges with labels 1 and 0 do not exceed 1. Euler’s polyhedral formula, which is related to polyhedron lines, nodes & faces, serves as the foundation for planar graph theory.  This paper focuses on exploring the divisor cordial labeling of certain classes of planar graphs obtained from complete graphs & complete bipartite graphs. We have explored these graphs for the graph operation, namely, vertex duplication, which is widely used in ensuring the data integrity.