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...

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 padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...

In this paper, we evaluate the uniqueness of several information-theoretic measures for graphs based on so-called information functionals and compare the results with other information indices and non-information-theoretic measures such as the well-known Balaban J index. We show that, by employing an information functional based on degree-degree associations, the resulting information index out...

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.

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...

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

(24) Ritter, G. L.; Isenhour, T. L. Minimal Spanning Tree Clustering of Gas Chromatographic Liquid Phases. Comput. Chem. 1977, 1, 145-153. Everitt, B. Cluster Analysis; Halsted: New York, 1974. Balaban, A. T. Chemical Graphs. XXXIV. Five New Topological Indices for the Branching of Tree-Like Graphs. Theor. Chim. Acra 1979, 53, 355-375. Balaban, A. T.; Motoc, I. Chemical Graphs. XXXVI. Correlati...