This book has been written covering basic knowledge of Fibonacci cordial labeling and 3-equitable labeling. The subject matter is presented in a vary simple, logical and relevant manner so that the readers understand it with right perspective. This book will prepare research scholar for various graph labeling techniques. in this book i have introduced one new labeling called Fibonacci cordial labeling. And i have also found some new graph and family of graphs which admits Fibonacci cordial and 3-equitable labeling.