Some remarks on Balaban and sum-Balaban index

The Maximum Balaban Index (Sum-Balaban Index) of Unicyclic Graphs

The Balaban index of a connected graph G is defined as J(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)DG(v) , and the Sum-Balaban index is defined as SJ(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)+DG(v) , where DG(u) = ∑ w∈V (G) dG(u,w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n v...

The Second Largest Balaban Index (Sum-Balaban Index) of Unicyclic Graphs

Balaban index and Sum-Balaban index were used in various quantitative structureproperty relationship and quantitative structure activity relationship studies. In this paper, the unicyclic graphs with the second largest Balaban index and the second largest SumBalaban index among all unicyclic graphs on n vertices are characterized, respectively.

On the Balaban Index of Trees

In this paper, we give a new proof that among all trees with n vertices, the star Sn and the path Pn have the maximal and the minimal Balaban index, respectively. This corrects some errors of proofs in [H. Dong, X. Guo, Character of graphs with extremal Balaban index, MATCH Commun. Math. Comput. Chem. 63 (2010) 799–812] and [L. Sun, Bounds on the Balaban index of trees, MATCH Commun. Math. Comp...

The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...

The Generalized Balaban Configurations