Fragmental graphs. A novel approach to generate a new family of descriptors. Applications to QSPR studies

Abstract

How an extension of definition of the adjacency concepts into graph theoretical framework can lead to a new family of graphs is shown in this article. A novel k-fragmental adjacency matrix is defined and its connection with vertex adjacent matrix of fragmental graph is presented. The analogous concept of vertex adjacency index of the molecular fragmental graph is also introduced. The molecular fragmental connectivity index kη(G) is defined in an analogous manner as Randic's molecular connectivity index [M. Randic, J. Am. Chem. Soc. 97 (1975) 6609]. The k-fragmental topological indices proposed are shown to be identical to the vertex connectivity indices of the molecular k-fragmental graph. Its ability to correlate with seven representative physical properties of 74 alkanes is proved. Standard statistical methods were used to obtain new QSPR models. The results were compared with the molecular connectivity indices of iterated line graphs. The QSPR models obtained with k-fragmental connectivity indices represent a significant improvement with respect to the molecular connectivity indices of iterated line graphs.