Enhancing D2C Business Models with Effective Hub Distribution Strategies and Triple Connected Certified Domination of Some Graph Operation

A dominating set S of a graph G is called a triple connected certified dominating set (TCCD-set) if for every vertex $v \in S,|N(v) \cap(V-S)| \neq 1$ and the subgraph $\langle S\rangle$ is triple connected. The minimum cardinality of a TCCDset is referred to as the triple connected certified domination number (TCCD-number), denoted by $\gamma_{T C C}(G)$. This study focuses on the operation $C_{n}\left(P_{m}\right)$ and $K_{n}\left(P_{m}\right)$ behavior of graphs concerning the triple connected certified domination number. The concept of a TCCD-set provides insights into graph connectivity and its applications in network reliability.In addition to graph theory, the study explores practical applications, such as establishing storage hubs in strategic city locations. These hubs support manufacturers using the direct-to-consumer (D2C) model, eliminating the need for intermediaries. This model not only streamlines the supply chain but also promotes environmental sustainability by optimizing resource use and reducing waste.