The Application of Mathematical Induction in Graph Theory——Concerning Graph Coloring Algorithm and Graph Isomorphism Problem
Graph theory's an important branch of mathematics,is closely related to combinatorics,control theory,operations research,and others.Among numerous research methods and technical means,mathematical induction is widely used in graph theory due to its powerful deduction and analysis capabilities.The mathematical induction is widely applied in graph theory as well.The basic content of graph theory involves graph staining algorithm and several related problems(including three-cycle graph with minimum vertex degree of 1 and complete graph with minimum number of edges),which can be solved with two different solutions,namely recursion and loop method.It can be said that mathematical induction is a powerful tool for solving graph theory problems,and that graph theory can be reasonably applied to effectively improve problem-solving efficiency,to reduce computation time,improve computational accuracy,and to make new breakthroughs in the field of graph theory.
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