Incidence graphs of bipartite G-graphs

Defining graphs from groups is a widely studied area motivated, for example, by communication networks. The most popular graphs defined by a group are Cayley graphs. G-graphs correspond to an alternative construction. After recalling the main properties of these graphs and their motivation, we propose a characterization result.With the help of this result, we show that the incidence graph of a symmetric bipartite G-graph is also a G-graph and we give a proof that, with some constraints, if the incidence graph of a symmetric bipartite graph is G-graph, the graph is also a G-graph. Using these results, we give an alternative proof for the fact that mesh of d-ary trees are G-graphs.