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Graph, degree, vertex

  1. Mar 9, 2008 #1
    Suppose A={x: x is an integer and 1 ≤ x ≤ 9}. Suppose G is a graph with V(G) = A x A, the Cartesian product of A with itself. What is V= lV(G)l ?
    Two vertices in G, (u,v) and (a,b) are adjacent if either: u=a, v=b, or ⌈u/3⌉=⌈a/3⌉ and ⌈b/3⌉.... List all of the vertices in G that are adjacent to the vertex (1,1). Recall that a graph is said to be regular of degree r if every vertex in the graph has degree r. Show that every vertex in G has the same degree. What is this degree of regularity? what is E= lE(G)l ?

    I know the first part up to finding the cartesian product... But I really don't know the second part of this question... help plz..
  2. jcsd
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