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.