فهرست نشریات علمی دسترسی آزاد ایران

In this survey the structure of one of the powerful group presentations, introduced by Alain Bretto is studied which is called $G$-graph. This survey contains some sections of properties, examples, characterization and groups automorphism of $G$-graphs. There are also some well-known graphs that have the structure of $G$-graphs. Moreover, in this survey we compare $G$-graph with the Cayley graph especially to examine the Hamiltonian property of such graphs for a given group. Furthermore by using the construction of a hypergraph, the spectra of the $G$-graph is reported. Finally, in the last section, the structure of the $G$-graph is considered as a network and connectivity property is studied.