Abstract
A general graph operation is defined and some of its applications are given in this paper. The adjacency spectrum of any graph generated by this operation is given. A method for generating integral graphs using this operation is discussed. Corresponding to any given graph, we can generate an infinite sequence of pair of equienergetic non-cospectral graphs using this graph operation. Given an orderenergetic graph, it is shown that we can construct two different sequences of orderenergetic graphs. A condition for generating orderenergetic graphs from non-orderenergetic graphs are also derived. This method of constructing connected orderenergetic graphs solves one of the open problem stated in the paper by Akbari et al.(2020).