CHEMICAL GRAPHS WITH DEGENERATE TOPOLOGICAL INDEXES BASED ON INFORMATION ON DISTANCES

Recently, four new types of vertex invariants, namely u, v, x, and y, were defined on the basis of information on graph distances. They were combined to give four highly selective topological indices: U, V, X, and Y. The degeneracy, i.e. equal values for nonisomorphic graphs, of the four topological indices is investigated. A structural condition and a graphical method which gives pairs of molecular graphs with identical U, V, X, and Y topological indices are introduced. The smallest pair of 4-trees representing alkanes having degenerated U, V, X, and Y values consists of trees with eighteen vertices.