The study of networks and graphs carried out by topological measures performs a vital role in securing their hidden topologies. This strategy has been extremely used biomedicine, cheminformatics bioinformatics, where computations dependent on graph invariants have made available to communicate the various challenging tasks. In quantitative structure–activity (QSAR) structure–property (QSPR) rel...

In this paper an algorithm for computing the Balaban and Randic indices of any simple connected graph was introduced. Also these indices were computed for IPR C80 fullerene isomers, Zigzag nanotubes and graphene by GAP program.

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. The PI index of a graph G is the sum of all edges uv of G of the number of edges which are not equidistant from the vertices u and v. In this paper we obtain the second and third extremals of catacondensed hexagonal systems with respect to the PI index.

The sum-connectivity index R′(G) of a graph G is the sum of the weights (du +dv) − 2 of all edges uv of G, where du and dv are the degrees of the vertices u and v in G. This index was recently introduced in [B. Zhou, N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46(2009), 1252–1270]. In this paper, we give the sharp lower bound of the sum-connectivity index of n-vertex unicyclic ...