Detour Domination Number of Some Cycle Related Graphs and its Role in the Installation of Electrical Appliances

Abstract

The detour distance  between two vertices of a connected graph  is the length of a longest path between them.  A set of vertices of  is called detour dominating set if every vertex of  is detour dominated by some vertex in. A detour dominating set of minimum cardinality is a minimum detour dominating set and its cardinality is the detour domination number. We present here a general class of a - regular Hamiltonian connected graph with. Moreover, we investigate the detour domination number of some cycle related graphs.