图的对称分割指数的界

Bounds of Symmetric Division Deg Index of Graphs

设G为n阶无向图,其顶点集V(G)=v_(1),v_(2),…,v_(n),d_(i)为顶点v_(i)的度,边集E(G),图G对称分割指数定义为SDD(G)=∑v_(i)v_(j)∈E(G)d_(i)d_(j)+d_(j)d_(i),反对称分割指数定义为ISDD(G)=∑v_(i)v_(j)∈E(G)d_(i)·d_(j)d^(2)_(i)+d^(2)_(j).应用图G的边数、最大度Δ、最小度δ等图不变量得到了图的对称分割指数SDD(G)的下界,并且对SDD(G)+ISDD(G),SDD(G)-ISDD(G),ISDD(G)/SDD(G)的关系进行了研究.

Let G be an undirected graph of order with vertex set and edge set E(G),and di be the degree of vertex vi.The sym V(G)={v_(1),v_(2),…,v_(n)}metric division deg index of a graph G was defined as SDD(G)=∑v_(i)v_(j)∈E(G)d_(i)d_(j)+d_(j)d_(i).The inverse symmetric division deg index of a graph G was defined as ISDD(G)=∑v_(i)v_(j)∈E(G)d_(i)·d_(j)d^(2)_(i)+d^(2)_(j).In this paper,some lower bounds of the symmetric division deg index SDD(G)of a graph G are obtained by using the graph invariants such as the number of edges,maximum degreeΔand minimum degreeδof graph G,and the relationship between SDD(G)+ISDD(G),SDD(G)-ISDD(G)and ISDD(G)/SDD(G)are studied.