Let $\mathcal{F}=\{F_{\alpha}: \alpha\in \mathcal{A}\}$ be a family of infinite graphs, together with $\Lambda$. The Factorization Problem $FP(\mathcal{F}, \Lambda)$ asks whether $\mathcal{F}$ can realized as factorization $\Lambda$, namely, there is $\mathcal{G}=\{\Gamma_{\alpha}: $\Lambda$ such that each $\Gamma_{\alpha}$ copy $F_{\alpha}$.We study this problem when either the Rado graph $R$ ...

It is known that determination problem of the bandwidth for an arbitrary graph is NP-complete. This paper establishes the bandwidth for the composition of a complete bipartite graph with other graphs; the strong product of a complete bipartite graph with a complete graph, a path, a cycle; and the tensor product of a complete graph with a complete graph.