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Let Gn be the simple graph with vertex set v0, v1, · · · , vn−1 such that viand vj are adjacent if and only if |j − i| ∈ {4, 5}. Draw the graphs G5 andG6. Determine the number of components of Gn.
Graph Theory

Let Gn be the simple graph with vertex set v0, v1, · · · , vn−1 such that viand vj are adjacent if and only if |j − i| ∈ {4, 5}. Draw the graphs G5 andG6. Determine the number of components of Gn.

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문제출처- 광주과학기술원(GIST) 최정옥 교수님의 “그래프 이론” 수업, 2024년 가을학기 중 Homework 2

Solution

(i). G_{5}

(ii). G_{6}

Number of connected components in Gn is
{n,if 0n4,9n,if 5n8,1,if n9.

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