In this article we study graphs with ordering of vertices, define a generalization called pseudoordering, and for graph $H$ the $H$-Hamiltonian number $G$. We will show that concept is both Hamiltonian traceable number. prove equivalent characteristics an isomorphism $G$ using Furthermore, fixed each path has maximal upper number, which same claim numbers numbers. Finally every connected only p...

The domatic partition problem seeks to maximize the partitioning of the nodes of the network into disjoint dominating sets. These sets represent a series of virtual backbones for wireless sensor networks to be activated successively, resulting in more balanced energy consumption and increased network robustness. In this study, we address the domatic partition problem in random geometric graphs ...