Analysing the structure of the automorphism groups of graphs, and investigating the properties of graphs that are constructed from algebraic structures are two important research topics in algebraic graph theory. Blending these two aspects of study, an algebraic intersection graph, called the invariant intersection graph of a graph, has been introduced in the literature. In this article, we study certain properties of the invariant intersection graph of a graph, and obtain some structural characterisations of these graphs, based on the automorphism group of the graph on which the invariant intersection graph is constructed.
Madhumitha et al. (Fri,) studied this question.