多项式是代数学中最基本的研究对象之一，而不可约多项式作为一种重要的多项

Polynomials are one of the most basic research objects in algebra. Irreducible polynomials are an important polynomial and are related to all polynomials. It has a status similar to prime numbers in integer rings in polynomial rings. Now the concept of reducibility has permeated all branches of mathematics, and there are different expressions in different branches. Therefore, studying the irreducibility of polynomials has very important theoretical significance and application value, which can help us solve many useful problems. <br>The research on the irreducibility of polynomials in the field of rational numbers has a long history and has been discussed in detail as the basic knowledge of linear algebra and higher algebra. Now, the research on irreducible polynomials in the field of rational numbers is still receiving much attention. The characteristic polynomial of a graph is a special kind of polynomial. The research on its irreducibility has certain reference significance for judging whether a rational coefficient polynomial can be reduced. <br>To determine the irreducibility of the characteristic polynomial of a graph, first determine the first coefficient, See if it is possible to use the modular m-reduced discriminant method, and if it meets the conditions, use this method to determine; regardless of the first coefficient, you can use the Eisenstein discriminant method to determine the irreducibility of the characteristic polynomial of the graph; and then scientifically Explore to see if you can find other ways to solve the irreducibility problem of the characteristic polynomial of the graph. Finally, according to the basic operation of Mathematica software, find the characteristic polynomials of seven point graphs, judge the reducibility of these polynomials, and draw conclusions.

Polynoun is one of the most basic research objects in modern mathematics, and as an important polynomial, it is related to all polynomials, and it has a status similar to the prime number in the integer ring in the polynomial ring. Now the concept of pactability has permeated the various branches of mathematics, with different forms of expression in different branches. Therefore, the study of polynomial irrelevance has very important theoretical significance and application value, which can help us solve many useful problems.<br>The study of polynomial non-covenant in rational number domain has a long history, and as the basic knowledge of linear algebra and high algebra is discussed in detail, and now, the study of unrelated polynomial polynomials on rational number domains is still a great concern. The characteristic polynomial of the graph as a special polynomial, the study of its unrelatability is of reference to judge whether the rational coefficient polynomial can be made.<br>Regarding the non-concimilation of the features of the graph, first determine the first coefficient, see if the model m-contracting method can be used, if the conditions are met, the method is used to determine; Finally, according to the basic operation of Mathematica software, the characteristic polynomials of seven dot plots are found, the pactability of these polynomials is judged and conclusions are drawn.

Polynomials are one of the most basic research objects in algebra. Irreducible polynomials, as an important kind of polynomials, are related to all polynomials. They have the similar position in polynomial rings as prime numbers in integer rings. Now the concept of reducibility has penetrated into every branch of mathematics, and it has different forms in different branches. So it is very important to study the irreducibility of polynomials, which can help us to solve many useful problems.<br>The irreducibility of polynomials in rational number field has been studied for a long time. As the basic knowledge of linear algebra and advanced algebra, the research on irreducible polynomials in rational number field is still concerned. As a special kind of polynomials, the study of irreducibility of the characteristic polynomials of graphs has certain reference significance for judging whether the rational coefficient polynomials are irreducible<br>To determine the irreducibility of the characteristic polynomials of a graph, first determine the first coefficient to see whether the modular m-reduction method can be used. If the conditions are met, use this method to determine; regardless of the first coefficient, use Eisenstein method to determine the irreducibility of the characteristic polynomials of a graph; then explore scientifically to see whether other methods can be found To solve the irreducibility of characteristic polynomials of graphs. Finally, according to the basic operation of Mathematica software, we find out the characteristic polynomials of seven point graphs, judge the reducibility of these polynomials, and draw a conclusion.<br>