Stabilizer Graph and Orbit Graph of Finite Groups
K. Annadurai, M. Bhuvaneshwari · Annals of Pure and Applied Mathematics · 2020
The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory.In this paper, we define new graphs namely stabilizer graph, orbit graph, non-stabilizer graph and non-orbit graph for each permutation group G. Our aim is to translate properties of graphs into algebraic properties and then using the results and methods of algebra to declare theorem about graphs.We investigate the interconnection between the group theoretic properties of G and the graph theoretic properties of the above said graphs.Some of the graphs are illustrated with example.Finally we obtain some important results including theorem and discuss the relationship between group isomorphism and graph isomorphism.