The bipartite edge frustration of graphs under subdivided edges and their related sums

The bipartite edge frustration of a graph GG, denoted by φ(G)φ(G), is the smallest number of edges that have to be deleted from GG to obtain a bipartite spanning subgraph of GG. This topological index is related to the well-known Max-cut problem, and has important applications in computing stability of fullerenes. In this paper, the bipartite edge frustration of an infinite family of fullerenes is computed. Moreover, this quantity for four classes of graphs arising from a given graph under different types of edge subdivisions is investigated.