Randić decomposition of catacondensed systems

Abstract

The Randić index of a simple graph G, denoted by χ, is defined as χ(G) = Σ_{1≤i≤j≤n-1} m_ij(G)/√ij where mij (G) is the number of edges in G connecting a vertex of degree i with a vertex of degree j. In this article we present a decomposition of C _h, the set of catacondensed systems with h hexagons, which contains complete information on the order relation induced by χ over C_h. In particular, the extremal χ-values of important subsets of C_h are determined.