In 2013, Madhavan Namboothiri N. M.

et al. introduced a class of Cayley fuzzy graphs induced by groups and studied the properties of the Cayley fuzzy graphs in terms of algebraic properties.

In this book, we generalized the results of Madhavan Namboothiri N. M.

et al. and proved that a bigger class of Fuzzy Cayley graphs could be induced by loops, weaker algebraic structures than groups.

Noura O. Alshehri and Muhammad Akram generalized the results of Madhavan Namboothiri N.

M. et al.

and introduced bipolar fuzzy Cayley graphs and derived graph properties in terms of algebraic properties. They also discussed connectedness in the Cayley bipolar fuzzy graph.

We generalized the results of Noura O. Alshehri1 and Muhammad Akram and investigated bipolar Cayley Fuzzy graphs induced by loops, and analogous results are derived.

The concept of Cayley Intuitionistic Fuzzy Graphs induced by loops is also included. In 2012, Anil Kumar V and Parameswarn Ashok Nair introduced the concept of Cayley digraph structures induced by groups and derived many interesting results.

Generalizations of Cayley digraph structures in weaker algebraic structures are also included in this book. .