  For the first time we represent every finite group in the form of a graph in
this book. The authors choose to call these graphs as identity graph, since the
main role in obtaining the graph is played by the identity element of the
group.
  This study is innovative because through this description one can immediately
look at the graph and say the number of elements in the group G which are
self-inversed. Also study of different properties, like the subgroups of a
group, normal subgroups of a group, p-sylow subgroups of a group and conjugate
elements of a group are carried out using the identity graph of the group in
this book.
  This book has four chapters. The first chapter is introductory. The second
chapter represents groups as graphs. In the third chapter, we have defined
similar types of graphs for algebraic structures like commutative semigroups,
loops, commutative groupoids and commutative rings. The final chapter poses 52
problems.
