S-coindex of some graph operations and its properties and conjugated polymers

The theory of chemical graphs is a field of mathematical chemistry that applies graph theory to the mathematical modeling of chemical phenomena. Topological index is a numerical descriptor of a molecule; it is found that there is strong correlation between the properties of chemical compounds and their molecular structure based on a specific topological feature of the corresponding molecular graph. The S-index of a graph is defined as the sum of five of the degree of vertices of a graph. In this paper, we introduce a new invariant of a graph which is identified as S-coindex. We study some basic mathematical properties and different types of graph operations like as Join, Cartesian Product, Composition, Tensor Product, Strong Product, Disjunction, Symmetric Difference, Corona Product of graphs.