Tensor products and strong products of soft graphs

Abstract

Molodtsov developed soft set theory in 1999 as an approach for modeling vagueness and uncertainty. Many academics currently employ soft set theory to solve decision-making problems. A parameterized point of view for graphs is provided using the idea of soft graphs. Soft graph theory is a rapidly growing field in graph theory because of its adaptability to parameterization techniques. In graph theory, the topic of graph products has attracted much attention. It is a binary operation on graphs that has many combinatorial applications. Analogous to the definitions of graph products, we can define product operations on soft graphs. In this paper, we introduce the tensor product, the restricted tensor product, the strong product, and the restricted strong product of soft graphs. We prove that these products of soft graphs are also soft graphs, and we derive formulas for finding vertex count, edge count, and the sum of part degrees in them.