Reference no: EM131446080

In the game of dominoes, two dominoes can be put end to end if the ends have the same number of dots on them. Each domino has two ends, each with some number of dots. A standard set of dominoes has one piece for each (unordered) pair of distinct integers from 0 to 6 inclusive, as well as one piece of the form (i, i) for each i from 0 to 6.For each of the following problems, (i) describe a graph we could build to answer the question. State how many vertices there are and under what criteria is there an edge (vi, vj ), and if that edge is directed or undirected; (ii) state which property of the graph would be present if and only if the answer is "yes,"and (iii) answer the question using your graph. You do not have to explicitly draw the graph, but you should still briefly justify your answer in graph-theoretic terms.(a) Is it possible to arrange all the dominoes into one big circle? (b) If all the pieces with no dots on one or both ends are excluded, is it possible to arrange the remaining pieces in a circle?