In this paper, we introduce some new versions based on the locating vectors named indices. particular, Hyper indices, Randić index, and Sambor index. The exact formulae for these indices of well-known families graphs Helm graph are derived. Moreover, determine importance 11 benzenoid hydrocarbons. Furthermore, show that have a reasonable correlation using linear regression with physicochemical ...

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. Let r(G) be the radius of G. We prove that for any connected graph G of maximum degree four which is not a path with even number of vertices, R(G) ≥ r(G). As a consequence, we resolve the conjecture R(G) ≥ r(G)− 1 given by Fajtlowicz in 1988 for the...

Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among gra...

A comparison of the performance of molecular descriptors of different types was conducted. The study was concentrated on determining which descriptors are included in the best linear multivariate regression models constructed for modeling various physicochemical properties (melting point, boiling point, refractive index, molar volume, and density) and biological activities (anaesthetic activity...

The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc (G) of a graph G is the mean value of eccentricities of all vertices of G. The harmonic index H (G) of a graph G is defined as the sum of 2 di+dj over all edges vivj of G, where di denotes the degree of a vertex vi in G. In this paper, we determine the unique tree with minimum average...