The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. index is utilized as tool study quantitative structure activity relationship (QSAR) structures property (QSPR) which correlate molecular its different properties activities. Graphs containing finite commutati...

qspr study on benzene derivatives have been made using recently introduced topological methodology. in this study the relationship between the randic' (x'), balaban (j), szeged (sz),harary (h), wiener (w), hyperwiener and wiener polarity (wp) to the thermal energy (eth), heat capacity (cv) and entropy (s) of benzene derivatives is represented.physicochemical properties are taken from the quantu...

Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E1(H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E1(H) = ∑u∈V(H) Symmetry 2016, 9, 7; doi: 10.3390/sym9010007 www.mdpi.com/journal/symmetry Article First and Second Zagreb Eccentricity Indices of Thorny Gra...

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors computed either from the molecular graph or from the three-dimensional (3D) molecular geometry. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, similarity and diversity assessment, and quantitative struct...

Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...