The Hosoya index of a graph is defined as the total number of the matchings (including the empty edge set) of the graph. In this paper, explicit formulas are given for the Hosoya index of bridge and splice graphs.

Among topological indices, Zagreb indices are very important, very old and they have many useful properties in chemistry and specially in mathematics chemistry. First and second Zagreb indices have been introduced by Gutman ...

The eccentric connectivity index of the molecular graph is defined as $zeta^c(G)=sum_{uvin E}degG(u)ε(u)$ , where degG(x) denotes the degree of the vertex x in G and ε(u)=max{d(x,u) |x ε V(G)}. In ...

A topological index is a function Top from Σ into real numbers with this property that Top(G) = Top(H), if G and H are isomorphic. Nowadays, many of topological indices were defined for different purposes. In the present ...

The eccentric distance sum is a graph invariant defined as $sum_{uvin E} εG(v)DG(v)$, where εG(v) is the eccentricity of a vertex v in G and DG(v ) is the sum of distances of all ...

Let G be a connected graph, the augmented eccentric connectivity index is a topological index was defined as $zeta(G)=sum_{i=1}^nM_i/E_i$, where Mi is the product of degrees of all vertices vj, adjacent to vertex ...