Biochemical and phylogenetic networks-I: hypertrees and corona products

Abstract

We have obtained graph-theoretically based topological indices for the characterization of certain graph theoretical networks of biochemical interest. We have derived certain distance, degree and eccentricity based topological indices for various k -level hypertrees and corona product of hypertrees. We have also pointed out errors in a previous study. The validity of our results is supported by computer codes for the respective indices. Several biochemical applications are pointed out.

An Analysis of Eccentricity‐Based Invariants for Biochemical Hypernetworks

“…e vertices of CBT(t) are designated in the following way: the label of root node is 1 and it is at level 0. For any vertex l, the children of l are tagged with 2l and 2l + 1 [28]. In a hypertree, extra edges are horizontal, where in the same level k, 1 ≤ k ≤ t, any two vertices are attached by an edge (see Figure 1).…”

“…In a hypertree, extra edges are horizontal, where in the same level k, 1 ≤ k ≤ t, any two vertices are attached by an edge (see Figure 1). Consider the hypertree CBT(3) in Figure 1 (see [28]) as an illustration to deduce distinct topological indices and their respective entropies. To demonstrate our main findings, we form a partition of edges of the hypertree CBT(t) for t levels established on eccentricity of end vertices in Tables 3 and 4 representing the edge partition of CBT(t).…”

“…Entropy. Now, using Tables 1 and 3, the fourth geometric arithmetic eccentric index is calculated in [28] as follows:…”

“…e Atom Bond Connectivity Entropy. Now, using Tables 1 and 4, the atom bond connectivity index is calculated in [28] as follows:…”

“…e Second Zagreb Eccentric Entropy. e second Zagreb eccentric index by using Tables 1 and 5 is calculated in [28] as follows:…”