Through this book, for the first time we represent every finite group in the form of a graph. 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. Merely for the sake of completeness we have defined similar type of graphs for algebraic structures like commutative semigroups, loops, commutative groupoids and commutative rings. This book has four chapters. Chapter one is introductory in nature. The reader is expected to have a good background of algebra and graph theory in order to derive maximum understanding of this research.
identity graphs, graphs, groups, neutrosophic logic
Smarandache, Florentin and W.B. Vasantha Kandasamy. "Groups as graphs." (2009). https://digitalrepository.unm.edu/math_fsp/219
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.