the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...

let g and h be two graphs. the corona product g o h is obtained by taking one copy of gand |v(g)| copies of h; and by joining each vertex of the i-th copy of h to the i-th vertex of g,i = 1, 2, …, |v(g)|. in this paper, we compute pi and hyper–wiener indices of the coronaproduct of graphs.

in this paper, a novel topological index, named m-index, is introduced based on expanded form of the wiener matrix. for constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. the usefulness of the m-index is demonstrated by several qspr/qsar models for different physico-chemical properties and biological activities of a large...

‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like bo...

the padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...