The circuit polynomial of the restricted rooted product G(Γ) of graphs with a bipartite core G

Vladimir R. Rosenfeld
2008 Discrete Applied Mathematics  
As an instance of the B-polynomial, the circuit, or cycle, polynomial P (G( ); w) of the generalized rooted product G( ) of graphs was studied by Farrell and Rosenfeld [Block and articulation node polynomials of the generalized rooted product of graphs, J. of Math. Sci. (India) 11 (1) (2000) 35-47] and Rosenfeld and Diudea [The block polynomials and block spectra of dendrimers, Internet Electron. J. Mol. Design 1(3) (2002) 142-156]. In both cases, the rooted product G( ) was considered without
more » ... ny restrictions on graphs G and . Herein, we present a new general result and its corollaries concerning the case when the core graph G is restricted to be bipartite.
doi:10.1016/j.dam.2006.06.015 fatcat:34x24snmvrcjpmt6hux7y3ursy