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Connectivity of particular graphs

Task number: 3958

Deremine the vertex and edge connectivity of the following graphs:

  • Variant

    Trees.

  • Variant

    Cycles and their complements.

  • Variant

    Complete bipartite graphs Km,n.

  • Variant

    Platonic solids.

  • Variant

    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.

  • Variant

    The toroidal grid Td(n) of dimension d for nd.

    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.

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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