Relations between the first and second Zagreb indices of subdivision graphs

Abstract

The first and second Zagreb indices of a graph are two of the topological invariants used in molecular calculations by Mathematicians and Chemists. First Zagreb index and multiplicative Zagreb indices, all versions of Zagreb indices of subdivision graphs, Zagreb indices of the line graphs of the subdivision graphs, Zagreb indices of subdivision graphs of double graphs, multiplicative Zagreb indices of graph operations were calculated and as a generalisation, the authors determined the multiplicative Zagreb indices of the r-subdivision of double graphs. In this paper, we obtain numerous new relations between the first and second Zagreb indices of the subdivision graphs of certain graph types.