Pair difference cordial labeling of some union of graphs

Let G = (V, E) be a (p, q) graph. Define ρ = {p/2 if p is even p−1/2 if p is odd and L = {±1, ±2, ±3, · · · , ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) − f(v)| such that ∆f1 − ∆fc1 ≤ 1, where ∆f1 and ∆fc1respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of the union of some graphs like path, cycle, star and bistar graph.Publisher's Versio

4-Prime cordiality of some cycle related graphs

Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wheel, gear, double cone, helm, closed helm, butterfly graph, and friendship graph