Mobius Cordial Labeling of Graphs

Let G = (V, E) be a simple graph with vertex set V and edge set E. A 1–1 function f : V → N is said to be a Mobius cordial labeling of the graph G if the induced edge function f∗ : E → {−1, 0, 1} is defined by \( {f}^{\ast }(uv)=\left|f\ (u)\hbox{--} f\ (v)\right| \) \( =n=\left\{\begin{array}{c}1\kern0.75em if\kern1em n=1\kern18.5em \\ {}{\left(-1\right)}^k\kern1em if\ n\ is\ a\ product\ of\ k\ distinct\ primes\kern2.5em \\ {}0\kern0.75em if\kern0.5em n\ has\ one\ or\ more\ repeated\ prime\ factors\ \end{array}\right. \) where uv ∈ E, satisfies the following conditions: Mobius cordial graphs are graphs that admit Mobius cordial labeling. In this chapter, the existence of the Mobius cordial labeling has been investigated to certain family of graphs.