Inverse Sum In-degree Index of Some Graphs and Their Squares

A topological index of a graph is a numeral value associated with a graph that fully uses it's topology and is invariant under graph isomorphism. There are certain important types of topological indices based on degree, distance, spectrum, and their mixed invariants. The inverse sum in-degree index (also known as ISI index) is one such degree-based topological index, defined with the intention that it may be useful in modeling molecular properties with higher accuracy than previously available descriptors. The ISI index of a graph da(vi)da(v) G is defined as ISI(G) (Formula Presented). In the similar line, the ISI-matrix (Formula Presented) of G is a square matrix where (Formula Presented) if (Formula Presented); and 0 otherwise. The = do(vi)+do(3) article explores the ISI index of several classes of graphs and their squares. Other than the ISI index, some results on spectral properties and the determinant of the ISI matrix are derived. The article also gives bounds for the ISI index of certain type of bipartite graphs.