Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...

Degeneracy is a word with two meanings. The popular usage of the word denotes deviance and decay. In scientific discourse, degeneracy refers to the idea that different pathways can lead to the same output. In the biological sciences, the concept of degeneracy has been ignored for a few key reasons. Firstly, the word "degenerate" in popular culture has negative, emotionally powerful associations...