By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

Abstract. For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as M1(G) = ∑ v∈V (G) dG(v) 2 and M2(G) = ∑ uv∈E(G) dG(u)dG(v), respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1(G) is ∑ uv∈E(G)(dG(u) + dG(v)). Recently Ashrafi, Došlić and Hamzeh introduced two related graphical invariants M...

Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative St...

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure–property relationships (QSPRs), and topological indices a valuable source of information about molecular properties, such as size, cyclicity, branching degree, symmetry. Graph theory has played crucial role the development dominating parameters descriptors. A molecule graph, under graph isomorphism...

In this paper, we study collective additive tree spanners for families of graphs enjoying special Robertson-Seymour’s tree-decompositions, and demonstrate interesting consequences of obtained results. We say that a graph G admits a system of μ collective additive tree r-spanners (resp., multiplicative tree t-spanners) if there is a system T (G) of at most μ spanning trees of G such that for any...

We obtain inequalities involving many topological indices in classical graph products by using the f-polynomial. In particular, we work with lexicographic product, Cartesian sum and first Zagreb, forgotten, inverse degree lordeg indices.

Measurements of graphs and retrieving structural information complex networks using degree-based network entropy have become an informational theoretical concept. This terminology is extended by the concept Shannon entropy. In this paper, we introduce with having edge weights which are basically redefined Zagreb indices. Some bounds calculated to idealize performance in limiting different kinds...

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

The concept of Zagreb eccentricity indices ( 1 E and 2 E ) was introduced in the chemical graph theory very recently. The eccentric connectivity index ( ) c ξ is a distance-based molecular structure descriptor that was used for mathematical modeling of biological activities of diverse nature. The second geometric-arithmetic index 2 ( ) GA was introduced in 2010, is found to be useful tool in QS...