A molecular graph is a graphical representation of a chemical structure which is constructed by using certain graph operation. Topological indices are global graph-theoretic parameters which are studied for molecular graphs and provide significant information related to physico-chemical properties of underlying chemical substances. Bipartite edge frustration is defined as the minimum number of edges whose deletion from the graph gives the bipartite spanning subgraph of given graph. Bipartite edge frustration is a topological index which is related to the chemical stability of various nanostructures such as Fullerenes. In this paper, the bipartite edge frustration of cactus chains are studied. We give an important conjecture generalizing this concept for whole family of cacti graphs at the end of the article.