图的ISDD指数的界

Bounds of ISDD Indices of Graphs

设G=(V(G),E(G))为n阶m条边的无向图,其顶点集为V(G)={v1,v2,…,vn},边集为E(G),G的反对称分割指数为ISDD(G)=∑_(v_(i)v_(j)(didj/d_(i)(2)+d_(j)^(2))).本文利用不等式及图的不变量对ISDD(G)和其他指数的关系进行了研究,得到了ISDD(G)的一些上、下界,并且证明了在一定条件下,ISDD(G)指数和对称分割指数SDD(G)是线性相关的.

Let G=(V(G),E(G))be an undirected graph with n vertices and m edges,its vertex set be V(G)={v1,v2,…,vn},and the edge set be E(G).The ISDD index of a graph G was defined as ISDD(G)=∑_(v_(i)v_(j)(didj/d_(i)(2)+d_(j)^(2))).In this paper,the relationship ISDD(G)with other indices was studied by using inequalities and graph invariants,and the new upper and lower bounds of the ISDD index of a graph were obtained,and it was proved that ISDD(G)and SDD(G)were linearly correlated under certain conditions.