Roman detour domination number of generalized hypercube networks

Generalized hypercube network is an interconnection network topology. The topology of interconnection network usually takes graph as a mathematical model, in which the vertex of graph represents the server and the edge of graph represents the connection between servers. As vertex count increases, the vertex degree of hypercube network increases as well. This has advantages, such as increased performance and reliability. The domination parameters are an important basis for analyzing and measuring the reliability of interconnection networks. In this paper, few properties of generalized hypercube network and Roman detour domination number for minimum dimensional generalized hypercube networks and hypercube networks are discussed. And also we determine the bounds for [Formula: see text] and [Formula: see text].