Fourth Order Connectivity Index of Polyphenylene Dendrimers

A simple graph G = (V, E) is a finite nonempty set V(G) of objects called vertices together with a (possibly empty) set E(G) of unordered pairs of distinct vertices of G called edges. In chemical graphs, the vertices of the graph correspond to the atoms of the molecule, and the edges represent the chemical bonds. Dendrimers are hyper-branched macromolecules, with a rigorously tailored architecture. They can be synthesized, in a controlled manner, either by a divergent or a convergent procedure. Their applications in chemistry, biology and nano-science are unlimited. A single number which characterizes the graph of a molecular is called a graph theoretical invariant or topological index. The connectivity index is one of the most popular molecular-graph. Recently, some researchers investigated m-order connectivity indices of some dendrimer nanostars, where m = 2 and 3. In this paper, the 4-order connectivity index of an infinite family of polyphenylene dendrimers is investigated.