The vertex graphical condensation for algebraic structure count of molecular graphs
Luzhen Ye · match Communications in Mathematical and in Computer Chemistry · 2021
The algebraic structure count of a bipartite graph G = (U, V ), denoted by L(G), is defined as the difference between the number of so-called "even" and "odd" Kekulé structures of G by Wilcox in theoretical organic chemistry.Let e = uv be an edge of a bipartite graph G. Gutman proved that G satisfies one of the following relations:where Ge (resp.Guv) is the graph obtained from G by deleting edge e (resp.vertices u and v).In this short note, we obtain a similar result and prove that for any u 1 , u 2 ∈ U, v 1 , v 2 ∈ V , G satisfies one of the following relations: