Embedding \((K_9-C_9)^n\) into interconnection networks

In the world of virtual and connected networks, the study of network’s computing capabilities through graph embedding has grown in prominence. In order to implement algorithms created for the guest graph in the host graph, embedding involves simulating one architecture, called the guest, into another, called the host. In this paper, we have obtained the optimal wirelength of embedding \((K_9-C_9)^n\) ${(K_9-C_9)}^n$ into Mesh \(M(3^n,3^n)\) $M(3^n,3^n)$ , generalized book graph \({\text {GB}}[9,3^{n-1},3^{n-1}]\) $\text{GB}[9,3^{n-1},3^{n-1}]$ and extended firecracker tree \({\text {EF}}_{9^n}\) ${\text{EF}}_{9^n}$ .