International Journal of Mathematics and Soft Computing Vol.4, No.2 (2014), 41 - 48. ISSN Print : 2249 - 3328 ISSN Online: 2319 - 5215 Prime cordial labeling of some special graph families G. V. Ghodasara H. & H. B. Kotak Institute of Science Rajkot, Gujarat, India. E-mail: gaurang enjoy@yahoo.co.in J. P. Jena L. E. College, Morbi Gujarat, India. E-mail: jasminjena.bls@gmail.com Abstract A bijection f from vertex set V of a graph G to {1, 2,..., |V |} is called a prime cordial labeling of G if each edge uv is assigned the label 1 if gcd(f (u),f (v)) = 1 and 0 if gcd(f (u),f (v)) > 1, where the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper we exhibit some new constructions on prime cordial graphs. Keywords: Petersen graph, fan, flower, cycle with triangle, prime cordial graph. AMS Subject Classification(2010): 05C78. 1 Introduction Graph labeling is a strong relation between numbers and structure of graphs. A useful survey to know about the numerous graph labeling methods is given by J. A. Gallian[5]. By combining the relatively prime concept in number theory and cordial labeling concept[4] in graph labeling, Sundaram et al.[10] introduced the concept called prime cordial labeling. A bijection f from vertex set V (G) to {1, 2,..., |V (G)|} of a graph G is called a prime cordial labeling of G if for each edge e = uv ∈ E, f ∗ (e = uv)=1; if gcd(f (u),f (v)) = 1 =0; if gcd(f (u),f (v)) > 1 then |e f (0) − e f (1)|≤ 1, where e f (0) is the number of edges labeled with 0 and e f (1) is the number of edges labeled with 1. In [1],[2],[9], the following graphs are proved to have prime cordial labeling: C n if and only if n ≥ 6; P n if and only if n =3 or 5; K 1,n (n odd); the graph obtained by subdividing each edge of K 1,n if and only if n ≥ 3. S. K. Vaidya et al.[11],[12],[13] proved that the square graph of path P n is a prime cordial graph for n =6 and n ≥ 8 while the square graph of cycle C n is a prime cordial graph for n ≥ 10. They also proved that the shadow graph of K 1,n for n ≥ 4, the shadow graph of B n,n for all n, certain cycle related graphs, the graphs obtained by mutual duplication of a pair of edges as well as mutual duplication of 41