Subgraphs can results through application of criteria based on matrix which characterize the entire graph. The most important categories of criteria are the ones able to produce connected subgraphs (fragments). Theoretical frame on graph theory, a series of three molecular fragmentation algorithms on pair of atoms, and construction of four square matrices (Szeged, Cluj, MaxF, and CMaxF) containing the fragment’s size are presented. New theoretical results on fragment’s size and the order based on sizes are presented. The obtained matrices were used to obtain the counting polynomials for two series of regular structures. The informational analysis on the obtained distinct counting polynomials was performed by using informational entropy and energy. Structure-property relationship analysis has been also conducted on the obtained counting polynomials. The obtained results are discussed and the main conclusions are highlighted.


Graph theory, Subgraphs, Graph polynomials, Entropy, Energy.