具有r个圈的仙人掌图关于距离-度指数的极值（英文）

Extremal Values on Distance-Degree-Based Topological Indices of Cacti with r Cycles

设G=(V,E)是一个连通图.G的基于距离-度的拓扑指数一般定义为 I_F(G)=∑{u,v}■VF(deg(u),deg(v),d(u,v)),其中F=F(x,y,z)是一个函数,deg(u)是顶点u的度,d(u,v)是u和v之间的距离.若F分别是(x+y)z,xyz,(x+y)z^(-1)和xyz^(-1),则IF(G)就分别是距离指数DD(G),Gutman指数Gut(G),和加权Harary指数H_A(G)与积加权Harary指数H_M(G).本文确定了具有r个圈的仙人掌图关于和加权Harary指数与积加权Harary指数的最大值,以及关于度距离指数与Gutman指数的最小值;并刻画了对应的极图.

Let G = （ V,E） be a connected graph. The distance-degree-based topological index is defined as the form IF（G） = ∑{u,v}？V F（ deg（ u） ,deg（ v） ,d（ u,v） ） , where F = F（ x, y, z） is a function, deg（ u） is the degree of u, and d（ u,v） the distance between u and v. If F are （ x ＋ y） z, xyz, （x ＋ y）z-1 and xyz-1, then IF（G） are the degree distance index DD（G）, the Gutman index Gut（G）, the additively weighted Harary index HA（G）, and the multiplicatively weighted Harary index HM （ G） , respectively. In this paper, we will determine the maximal values of the additively weighted Harary index, the multiplicatively weighted Harary index and the minimal value of the degree distance index, the Gutman index among all cacti of order n with r cycles, and characterize the corresponding extremal graphs.