【摘要】 为了研究具有最小匹配能量的广义仙人掌图的结构,利用一些图形变换对图的匹配能量产生影响的相关方法,得到了具有最小匹配能量的广义仙人掌图的结构:在所有顶点数、边数、块为圈的数目和块为双圈图的数目都固定的广义仙人掌图中,G*(n,m,r,s)是匹配能量最小的图;在所有顶点数和边数都固定的广义仙人掌图中,G*(n,m,1,(m-n)/2)或G*(n,m,0,(m-n+1)/2)是匹配能量最小的图。更多还原

【Abstract】 Some methods of graph-transformation which have effect on matching energy were used to discuss the generalized cacti graph with the minimum matching energy was determined. In this paper,the generalized cacti graph with the minimum matching energy was determined: G*( n,m,r,s) has minimum matching energy in the set of generalized cacti graphs with the xed numbers of vertices,edges,the blocks each of which is a cycle and the blocks each of which is a bicyclic graph; G*( n,m,1,( m- n) /2) or G*( n,m,0,( m- n + 1) /2) has the minimum matching energy in the set of generalized cacti graphs with the xed numbers of vertices and edges.更多还原