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Giải bài 4 trang 43 Chuyên đề học tập Toán 11 Cánh diều

Tìm bậc của mỗi đỉnh và chỉ ra một chu trình Hamilton (nếu có) của đồ thị ở Hình 21.

Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - ℱCánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tìm bậc của mỗi đỉnh và chỉ ra một chu trình Hamilton (nếu có) của đồ thị ở Hình 21.

Phương pháp giải - Xem chi tiết

Bậc của một đỉnh A trong đồ thị G là số cạnh của đồ thị nhận đỉnh A làm đầu mút, kí hiệu là \(d(A)\) Trong đồ thị, một đường đi được gọi là đường đi Hamilton nếu đường đi đó đi qua tất cả các đinht của đồ thị, mỗi đỉnh đúng 1 lần. Nếu chu trình là đường đi Hamilton thì chu trình đó được gọi là chu trình Hamilton.

Lời giải chi tiết

Ta có: d(A) = 3, d(B) = 3, d(🅺C) = 4, d(D) = 4, d(E) = 2.

Vì đồ thị ở Hình 21 gồm có 5 đỉnh nên tổng bậc của hai đỉnh không kề nhau bất kì đều không nhỏ hơn 5. Do đó, theo định lí Ore, đồ thị này có ít nhất một chu🎃 trình Hamilton.

Một chu trình Hamilton của đồ thị này là ABCEDA.

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