The Szeged index of a graph G, denoted by S z(G) = ∑ uv=e∈E(G) nu (e)n G v (e). Similarly, the Weighted Szeged index of a graph G, denoted by S zw(G) = ∑ uv=e∈E(G) ( dG(u)+ dG(v) ) nu (e)n G v (e), where dG(u) is the degree of the vertex u in G. In this paper, the exact formulae for the weighted Szeged indices of generalized hierarchical product and Cartesian product of two graphs are obtained.

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

in this paper, some applications of our earlier results in working with chemical graphs arepresented.

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...