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Connectivity of particular graphs
Task number: 3958
Deremine the vertex and edge connectivity of the following graphs:
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Trees.
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Cycles and their complements.
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Complete bipartite graphs Km,n.
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Platonic solids.
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Hypercube Qd of dimension d.
Vertices of Qd are all strings of length d consiting of zeros and ones. Two vertices are connected by an edge if the strings differ in exactly one position.
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The toroidal grid Td(n) of dimension d for n≫d.
Vertices of Td(n) are arithmetic vectors from Zdn. Two vectors are adjacent, if their difference has in exactly one component ±1 and elsewhere zeroes.
Hence T1(n) is a cycle on n vertices, T2(n) is a grid n×n with the left side glued to the right and the top side glued to the bottom.