in this paper we present explicit formulas for the eccentric connectivity index of three classesof chain hexagonal cacti. further, it is shown that the extremal chain hexagonal cacti withrespect to the eccentric connectivity index belong to one of the considered types. some openproblems and possible directions of further research are mentioned in the concluding section.

in this paper, we calculate the eccentric connectivity index and the eccentricity sequence of two infinite classes of fullerenes with 50 + 10k and 60 + 12k (k in n) carbon atoms.

In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.

In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.

Abstract The m-order connectivity index mχ(G) of an organic molecule whose molecular graph is G is the sum of the weights (di1di2 · · · dim+1) 1 2 , where di1di2 · · · dim+1 runs over all paths of length m in G and di denotes the degree of vertex vi. Dendrimer is a polimer molecule with a distinctive structure that resembles the crown of a tree. Dendrimers are key molecules in nanotechnology an...

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 degreeof vertex u. in this paper we present some bounds of this new topological index.