湖南文理学院学报（自然科学版）
湖南文理學院學報（自然科學版）
호남문이학원학보（자연과학판）
JOURNAL OF HUNAN UNIVERSITY OF ARTS AND SCIENCE(SCIENCE AND TECHNOLOGY)
2012年
1期
24-27,35
,共5页
扩展离心连通指数(Aξc(G))%树%单圈图%极值图
擴展離心連通指數(Aξc(G))%樹%單圈圖%極值圖
확전리심련통지수(Aξc(G))%수%단권도%겁치도
The augmented eccentric connectivity index(Aξc(G))%Trees%Unicyclic graphs%Extremal graphs
设图G=G(V,E)是简单图.图扩展离心连通指数Aξc(G)是基于邻接和的指数,即Aξc(G)=∑u∈V(G)Πv∈N(u)d(v)/e(u)其中e(u)为图顶点u的离心率,N(u)为顶点u的邻点集.本文刻画了树中具有最大、第二大、 最小、第二小扩展离心连通指数的树的特征和单圈图中具有最大扩展离心连通指数的单圈图的特征.
設圖G=G(V,E)是簡單圖.圖擴展離心連通指數Aξc(G)是基于鄰接和的指數,即Aξc(G)=∑u∈V(G)Πv∈N(u)d(v)/e(u)其中e(u)為圖頂點u的離心率,N(u)為頂點u的鄰點集.本文刻畫瞭樹中具有最大、第二大、 最小、第二小擴展離心連通指數的樹的特徵和單圈圖中具有最大擴展離心連通指數的單圈圖的特徵.
설도G=G(V,E)시간단도.도확전리심련통지수Aξc(G)시기우린접화적지수,즉Aξc(G)=∑u∈V(G)Πv∈N(u)d(v)/e(u)기중e(u)위도정점u적리심솔,N(u)위정점u적린점집.본문각화료수중구유최대、제이대、 최소、제이소확전리심련통지수적수적특정화단권도중구유최대확전리심련통지수적단권도적특정.
Let G = (V, E) be a simple graph and the augmented eccentric connectivity index is an adjacency-sum-distance based index by denote Aξc(G) , is defined as Aξc(G)=∑u∈V(G)Πv∈N(u)d(v)/e(u) where e(u) is its eccentricity of vertex u.In this paper, the trees with first, second minimum and maximum (Aξc(G))are characterized and the unicyclic graphs with maximum (Aξc(G)) are characterized.
