一类双圈图的匹配能量和Hosoya指标排序  

The order of matching energy and Hosoya index of a classes of bicyclic graphs

作　　者：马海成[1] 李丹阳 解承玲 MA Haicheng;LI Danyang;XIE Chengling(School of Mathematics & Statistics,Qinghai Nationalities University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,青海西宁810007

出　　处：《厦门大学学报（自然科学版）》2021年第4期735-740,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11561056,11661066);青海省自然科学基金(2016-ZJ-914)。

摘　　要：路Ps+2的两个端点分别与圈Ga+1和Cb+1上的一个点黏结后得到的连通图称为哑铃图,记为∞(a,s,b),这里的s≥0,a≥2,b≥2.—个图的匹配多项式的所有根绝对值的和称为这个图的匹配能量,一个图的匹配多项式的所有系数绝对值的和称为这个图的Hosoya指标.本文给出了哑铃图∞(a,s,b)在a和b两个变量变化下的匹配能量的全排序和Hosoya指标的全排序.作为推论,找到了哑铃图∞(a,s,b)在a和b两个变量变化下的匹配能量(Hosoya指标)取得极值的图.Let Ps+2,Ca+1 and Cb+1 be a path with s+2 vertices,two cycles with a+1 vertices and b+1 vertices,respectively.The dumbbell shape graphs∞(a,s,b)is the graph with a+b+s+2 vertices obtained from Ps+2∪Ca+1∪Cb+1 by identifying two end vertices of Ps+2 with a vertex of Ca+1 and a vertex of Cb+1,respectively,where s≥0,a≥2,and b≥2.Let G denote a graph and letμ(G,x)denote the matching polynomial of G.The sum of the absolute values of all the roots ofμ(G,x)is called the matching energy,denoted as EM(G),whereas the sum of the absolute values of all the coefficients ofμ(G,x)is called the Hosoya index,denoted as Z(G).In the paper,we give a complete order of matching energy and Hosoya index of the dumbbell shape graphs∞(a,s,b),with varible a and b.As a byproduct,the corresponding extreme graphs are also described.

关 键 词：哑铃图∞(a s b) 匹配多项式 匹配能量 HOSOYA指标 

分 类 号：O157.5[理学—数学]