- k-PRIME CORDIAL GRAPHS
- PONRAJ, R. ; SINGH, RAJPAL ; KALA, R. ; NARAYANAN, S. SATHISH ;
- Journal of applied mathematics & informatics, volume 34, issue 3_4, 2016, Pages 227~237
- DOI : 10.14317/jami.2016.227

Abstract

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_{f} (i) − v_{f} (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_{f} (0) − e_{f} (1)| ≤ 1 where v_{f} (x) denotes the number of vertices labeled with x, e_{f} (1) and e_{f} (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.