Study of the Bipartite Edge Frustration of Graphs
The smallest number of edges that have to be deleted from a graph to obtain a bipartite spanning subgraph is called the bipartite edge frustration of G and denoted by φ(G). This topological index is related to the well-known Max − cut problem, and has important applications in computing stability of fullerenes. In this paper we determine the bipartite edge frustration of some classes of composite graphs. Moreover, this quantity for four classes of graphs arising from a given graph under different types of edge subdivisions is investigated.
KeywordsBipartite Graph Black Vertex Root Vertex Composite Graph Chain Graph
- Cvetković DM, Doob M, Sachs H (1980) Spectra of graphs– theory and application. Academic, New YorkGoogle Scholar
- Došlić T (2005b) Splices, links, and their valence-weighted Wiener polynomials. Graph Theory Notes NY 48:47–55Google Scholar
- Ghojavand M, Ashrafi AR (2008) Computing the bipartite edge frustration of some nanotubes. Digest J Nanomater Bios 3:209–2014Google Scholar
- Imrich W, Klavžar S (2000) Product graphs, structure and recognition. Wiley, New YorkGoogle Scholar
- West DB (1996) Introduction to graph theory. Prentice-Hall, Upper Saddle RiverGoogle Scholar