Discrete Mathematics: Applied Combinatorics and Graph Theory

a₁ algorithm balls per cell BASIS STEP C₁ C₂ chromatic number coefficient colors combinatorial connected graph Consider Figure contains counting definition degree determining the number dice digit directed graph distinct cells elements equivalent Eulerian circuit Example Exercises exponential generating function factor Find a recurrence graph G graph in Figure Graph Theory Hamiltonian cycle Hamiltonian path hence identical balls inclusion-exclusion principle induction hypothesis induction step initial conditions integer equation integer solutions intersection isomorphic least mathematical induction minimal spanning tree multiple multiset natural numbers number of balls number of edges number of integer number of solutions number of vertices number of zeros objects obtain odd number one-one correspondence P₁ pair partition planar simple graph polynomial postfix expressions problem proof Proposition Prove recurrence relation rule of product rule of sum simple graph subsets techniques true v₁ vertex weighted graph well-ordering property X₁