Vertex and Edge Type Relations of Randic Index for Chemical Trees

Abstract

Let $T$ be a chemical tree, i.e. a tree with all vertices of degree less than or equal to $4$. We find relations for the $0$-connectivity and $1$-connectivity indices ${}^0\chi (T)$ and ${}^1\chi (T)$, respectively, in terms of the vertices and edges of $T$. A comparison of these relations with the coefficients of the characteristic polynomial of $T$ associated to its adjacency matrix is established.