Thel middlel graphl ofl al graphl G,l denotedl byl M(G)l isl al graphl whosel vertexl setl isl V(G)∪E(G)l l andl twol verticesl arel adjacentl ifl theyl arel adjacentl edgesl ofl Gl orl onel isl al vertexl andl otherl isl anl edgel incidentl withl it.l Al dominatingl setl Dl ofl M(G)l isl calledl al restrainedl dominatingl setl ofl M(G)l ifl everyl vertexl notl inl Dl isl adjacentl tol al vertexl inl Dl andl tol al vertexl inl V[M(G)]-D.l Thel minimuml cardinalityl ofl l Dl isl calledl thel restrainedl dominationl numberl ofl M(G)l andl l isl denotedl byl γ_(rl ) [M(G)].