the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

The relationship between the Randic , Wiener, Hosoya , Balaban, Schultz indices, Harary numbers andDistance matrix to enthalpies of formation (Airf), heat capacity, (Cp) , enthalpies of combustion (AH °c ),enthalpy of vaporization (AH °vap) and normal boiling points (bpK)of C2 C10 normal alkanes isrepresented

the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.

The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

The sum of distances between all the pairs of vertices in a connected graph is known as the {it Wiener index} of the graph. In this paper, we obtain the Wiener index of edge complements of stars, complete subgraphs and cycles in $K_n$.

In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms dG(u)+dG(v) over all edges uv∈E(G) , where dG(u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds for the multiplicative sum Zagreb index of several graph operations such as union, join, corona product, composition, direct product, Cartesian product and strong pro...