Broadcasting　is　a　common　and　basic　operation　used　to　support　various　network　protocols　in　wireless　networks.　To　achieve　energy-efficient　broadcasting　is　especially　important　for　ad　hoc　wireless　sensor　networks　because　sensors　are　generally　powered　by　batteries　with　limited　lifetimes.　Energy　consumption　for　broadcast　operations　can　be　reduced　by　minimizing　the　number　of　relay　nodes　based　on　the　observation　that　data　transmission　processes　consume　more　energy　than　data　reception　processes　in　the　sensor　nodes,　and　how　to　improve　the　network　lifetime　is　always　an　interesting　issue　in　sensor　network　research.　The　minimum-energy　broadcast　problem　is　then　equivalent　to　the　problem　of　finding　the　minimum　Connected　Dominating　Set　(CDS)　for　a　connected　graph　that　is　proved　NP-complete.　In　this　paper,　we　introduce　an　Efficient　Minimum　CDS　algorithm　(EMCDS)　with　help　of　a　proposed　ordered　sequence　list.　EMCDS　does　not　concern　itself　with　node　energy　and　broadcast　operations　might　fail　if　relay　nodes　are　out　of　energy.　Next　we　have　proposed　a　Minimum　Energy-consumption　Broadcast　Scheme　(MEBS)　with　a　modified　version　of　EMCDS,　and　aimed　at　providing　an　efficient　scheduling　scheme　with　maximized　network　lifetime.　The　simulation　results　show　that　the　proposed　EMCDS　algorithm　can　find　smaller　CDS　compared　with　related　works,　and　the　MEBS　can　help　to　increase　the　network　lifetime　by　efficiently　balancing　energy　among　nodes　in　the　networks.