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adjacent arrangements assigned balls binary tree binomial bipartite graph breadth first search chosen coefficient coins color combinatorics Compute the number connected graph consecutive Consider contains count the number counting procedure denote Describe an algorithm different objects digits directed graph elements equal equation equivalence classes Eulerian circuit Example exponential generating function Find the number formula four graph G graph theory Hamiltonian cycle Hamiltonian path identical induction juggler labeled least lexicographic order Multiplication Principle number of different number of distributions number of edges number of objects number of outcomes number of partitions number of sequences obtain path permutations planar graph polynomial positive integer possible Principle of Inclusion-Exclusion problem Proof properties Puzzle recurrence relation represented satisfy Section selection sequences of length Show simple graph solve spanning tree subgraph summands SUPPLEMENTARY COMPUTER PROJECTS Suppose THEOREM total number unlimited repetition vertex weighted graph Write a program