Atom-bond-connectivity index of certain graphs

The ABC index is one of the most applicable topological graph indices and several properties of it has been studied already due to its extensive chemical applications. Several variants of it have also been defined and used for several reasons. In this paper, we calculate the atom-bond connectivity index of some derived graphs such as double graphs, subdivision graphs and complements of some standard graphs.Publisher's Versio

Exponential fraction index of certain graphs

Topological indices play a great role in Mathematical chemistry. Many graph theorists as well as chemists attracted towards these molecular descriptors. The aim of this paper is to introduce and investigate the Exponential Fraction index (a degree based Topological index). It is defined as follows. EF(G) = Σ uv∈E(G) edu/dv . Here du and dv are the maximum and minimum degree respectively. In this paper, we calculate the Exponential Fraction index of double graphs, subdivision graphs and complements of some standard graphs. Also we compute the index for chemical structures Graphene and Carbon nanocones.Publisher's Versio

On certain topological indices of the derived graphs of subdivision graphs

The derived graph [G]† of a graph G is the graph having the same vertex set as G, with two vertices of [G]† being adjacent if and only if their distance in G is two. Topological indices are valuable in the study of QSAR/QSPR. There are numerous applications of graph theory in the field of structural chemistry. In this paper, we compute generalized Randi´c, general Zagreb, general sum-connectivity, ABC, GA, ABC4, and GA5 indices of the derived graphs of subdivision graphs.Publisher's Versio

Inverse problem for Albertson irregularity index

Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to Show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publisher's Versio

Inverse problem for Albertson irregularity index

Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to Show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publisher's Versio

Geometric-arithmetic Index and Zagreb Indices of Certain Special Molecular Graphs

In this paper, we determine the Geometric-arithmetic indexand Zagreb indicesof fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs