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  • 有一棵樹(shù),度數(shù)為3的結(jié)點(diǎn)數(shù)N1,度數(shù)為2的結(jié)點(diǎn)數(shù)N2,其余為葉子,有幾片葉子?

    有一棵樹(shù),度數(shù)為3的結(jié)點(diǎn)數(shù)N1,度數(shù)為2的結(jié)點(diǎn)數(shù)N2,其余為葉子,有幾片葉子?
    最好有具體過(guò)程
    數(shù)學(xué)人氣:574 ℃時(shí)間:2020-05-19 16:30:55
    優(yōu)質(zhì)解答
    N1+2片葉子.
    設(shè)有x片葉子,則此樹(shù)有N1+N2+x個(gè)節(jié)點(diǎn),樹(shù)的邊數(shù)比節(jié)點(diǎn)數(shù)少1,是N1+N2+x-1條邊,由握手定理,3×N1+2×N2+x×1=2(N1+N2+x-1),解得x=N1+2,所以有N1+2片葉子.??????????????30???????д????Щ??????и??????????????????ɡ??????????x????????????n????????m????m=n-1??n=N1+N2+x??m=N1+N2+x-1???????????????????????????2????????3??N1+2??N2+x??1=2(N1+N2+x-1)??3N1+2N2+x=2N1+2N2+2x-2????x=N1+2?????????????N1+2?????
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