Edge corona product and its topological descriptors with applications in complex molecular structures

Abstract

Graph operations offer a robust framework that enables the analysis, modeling, and resolution of intricate problems. Their versatility and broad range of applications make them essential across numerous fields of study and research, playing an irreplaceable role in tackling complex challenges. A topological index is a real number associated with a graph that gives insight into the topological properties of the graph. There are numerous topological indices in this era now, with three variants like degree based, distance based and eccentricity based topological indices. In this paper, we studied a well known graph operation named as edge corona product and investigate their some degree based topological indices. As applications, this graph operations can be used to study topological properties of complex structure of linear and cyclic silicate networks, together with triangular and double triangular networks. Some existing results in the literature can be obtained as corollaries of the new results. A conjecture is proposed relating the general first Zagreb index of the edge corona product of two graphs.