Inverse Sum Indeg Index Research Articles

Some results on the inverse sum indeg index of a graph

The inverse sum indeg index, which was selected in Vukičević (2010) [14] as a significant predictor of total surface area of octane isomers and for which the extremal graphs obtained with the help of MathChem have a particularly simple and elegant structure, is defined as ISI(G)=∑uv∈E(G)dudvdu+dv, where du is the degree of the vertex u of G. Recently, Falahati-Nezhad, Azari and Došlić (2017) [3] gave several sharp upper and lower bounds on this index in terms of some molecular structural parameters such as the order, size, radius, number of pendant vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree, and related this index to several well-known molecular descriptors. In this paper, we present sharp bounds for the inverse sum indeg index for graphs with given matching number, independence number and vertex-connectivity, and we also characterize all extremal graphs for which those bounds are obtained.

The inverse sum indeg index of graphs with some given parameters

Let [Formula: see text] be a simple connected graph. The inverse sum indeg index of [Formula: see text], denoted by [Formula: see text], is defined as the sum of the weights [Formula: see text] of all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the degree of a vertex in [Formula: see text]. In this paper, we derive some bounds for the inverse sum indeg index in terms of some graph parameters, such as vertex (edge) connectivity, chromatic number, vertex bipartiteness, etc. The corresponding extremal graphs are characterized, respectively.

On Topological Indices of Sudoku Graphs and Titania TiO2 Nanotubes

In this paper, we obtain the exact formulae for some topological indices such as the general sum-connectivity index, atom-bond connectivity index, geometric arithmetic index, inverse sum indeg index, symmetric division deg index and harmonic polynomial of titania TiO2 Nanotubes and Sudoku graphs.

Inverse sum indeg index of graphs

The inverse sum indeg index ISI(G) of a simple graph G is defined as the sum of the terms dG(u)dG(v)dG(u)+dG(v) over all edges uv of G, where dG(u) denotes the degree of a vertex u of G. In this paper, we present several upper and lower bounds on the inverse sum indeg index in terms of some molecular structural parameters and relate this index to various well-known molecular descriptors.

On relations between inverse sum indeg index and multiplicative sum Zagreb index

On relations between inverse sum indeg index and multiplicative sum Zagreb index

Sharp bounds on the inverse sum indeg index

The inverse sum indeg index is a recently-introduced bond-additive descriptor that was selected by Vukičević and Gašperov (2010) as a significant predictor of total surface area of octane isomers. In this paper, we present several sharp upper and lower bounds on the inverse sum indeg index in terms of some graph parameters such as the order, size, radius, number of pendant vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree, and relate this index to various well-known graph invariants such as the ordinary and multiplicative Zagreb indices, Randić indices, sum-connectivity index, modified Zagreb index, harmonic index, forgotten index, and eccentric connectivity index.

On the inverse sum indeg index

Discrete Adriatic indices have been defined by Vukičević and Gašperov (2010), as a way of generalizing well-known molecular descriptors defined as the sum of individual bond contributions, such as the second Zagreb index or the Randić index. Among the 148 discrete Adriatic indices analyzed by Vukičević and Gašperov on the benchmark datasets of the International Academy of Mathematical Chemistry, 20 indices were selected as significant predictors of physicochemical properties.Here we study graph-theoretical properties of the Inverse Sum Indeg index, which was selected as a significant predictor of total surface area of octane isomers, and determine extremal values of this index across several graph classes, including connected graphs, chemical graphs, trees and chemical trees.