Get Help-Assignment (AMA)

Get Help-Assignment (AMA)

Assignment (AMA)


Q3: Two opposite corners are removed from an 8-by-8 checkerboard. Prove that it is impossible to cover the remaining 65 squares with 31 dominoes, such that each domino covers two adjacent squares?




Q3: Through A Write an algorithm to construct the indicated graph operation, using only the primary graph operations of additions and deletions of vertices and edges. Test your algorithm on the pair ( P4, W5 ) and on the pair ( K4 – K2, C4 ):

  • Cartesian product of two graphs (psedocode)?


Q4: Through A,B either draw the required graph or explain why no such graph exists:

  • An 8-vertex, 2-component, simple graph with exactly 10 edges and three cycles?
  • An 11-vertex, simple, connected graph with exactly 14 edges that contains five edge-disjoint cycles?


Q5: Prove or disprove: If a simple graph G has no cut-edge, then every vertex pf G has even degree?


Q6: Prove that if a graph has exactly two vertices of odd degree, then there must be a path between them?


Q7: Show that any nontrivial simple graph contains at least two vertices that are not cut-vertices?


Q8: Through A Draw the specified tree(s) or explain why on such a tree(s) can exist?

  • A 14-vertex binary tree of height 3.


Q9: Prove that a directed tree that has more than one vertex with in degree 0 cannot be a rooted tree?

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