Matching Integral Graphs withSmall-Diameter

令G是n个顶点的图。匹配整图表示的是匹配多项式的根都是整数的图。本文运用路树的相关概念，通过将树的一些分支进行路径收缩得到带有圈的匹配整图，利用这种方法构造了一些直径为4,5,6的匹配整图。Let G be a graph with n vertices. Matching integral graphs are defined as graphs where all roots of the matching polynomial are integers. In this paper, by applying concepts related to path-trees and contracting some branches of a tree into paths, we derive matching integral graphs that contain cycles.Using this approach, we construct several matching integral graphs with diameters 4, 5, and 6.