“…1- 14 The minimum connected dominating set (MCDS) of the network topology graph forms a virtual backbone by which the routing overhead can be significantly reduced, where the number of vertices responsible for the route discovery and data transmission can be reduced to the 6,9,12-16 A WCDS of a graph G is a dominating subset of G so that the vertex set of the given subset and all the vertices with at least one endpoint in the subset induce a connected sub-graph of G. Finding the WCDS 1,2,4-6,8,10 is a well-known approach for clustering the wireless ad hoc networks, 17,[18][19][20][21][22][23][24][25] and was first proposed by Chen and Listman in Ref. 4.…”