Recent Advancements in Graph Theory

6SD-Prime Cordial Labeling of Double k-Polygonal Snake Graph

U. M. Prajapati

Department of Mathematics,St. Xavier’s College,Ahmedabad, Gujarat (INDIA)E-mail: [e-mail]

A. V. Vantiya

Department of Mathematics,Gujarat University,Ahmedabad, Gujarat (INDIA)E-mail: [e-mail]

Let f: V (G) → {1, 2, …, |V (G)|} be a bijection, and let us denote S = f(u) + f(v) and D = |f(u) − f(v)| for every edge uv in E(G). Let f′ be the induced edge labeling, induced by the vertex labeling f, defined as f′: E(G) → {0, 1} such that for any edge uv in E(G), f′(uv) = 1 if gcd(S, D) = 1, and f′(uv) = 0 otherwise. Let e_f′(0) and e_f′(1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e_f′(0) − e_f′(1)| ≤ 1 ...