湖南师范大学自然科学学报
湖南師範大學自然科學學報
호남사범대학자연과학학보
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS NORMALIS HUNANENSIS
2009年
3期
23-26
,共4页
化学图%线图%Wiener指数%圈秩
化學圖%線圖%Wiener指數%圈秩
화학도%선도%Wiener지수%권질
chemical graph%line graph%Wiener index%cyclomatic number
图G=(V,E)的Wiener指数W(G)是一个基于距离的拓扑指数,它是G中所有顶点之间的距离之和.对于任意整数n,证明了存在无限多个圈秩为2平面二部化学图,其Wiener指数与它的线图的Wiener指数之差是n,且其线图也是化学图;部分解决了A.D.Dobrynin和L.S.Mernikow提出的一个公开问题.
圖G=(V,E)的Wiener指數W(G)是一箇基于距離的拓撲指數,它是G中所有頂點之間的距離之和.對于任意整數n,證明瞭存在無限多箇圈秩為2平麵二部化學圖,其Wiener指數與它的線圖的Wiener指數之差是n,且其線圖也是化學圖;部分解決瞭A.D.Dobrynin和L.S.Mernikow提齣的一箇公開問題.
도G=(V,E)적Wiener지수W(G)시일개기우거리적탁복지수,타시G중소유정점지간적거리지화.대우임의정수n,증명료존재무한다개권질위2평면이부화학도,기Wiener지수여타적선도적Wiener지수지차시n,차기선도야시화학도;부분해결료A.D.Dobrynin화L.S.Mernikow제출적일개공개문제.
The Wiener index W(G) of a graph G = (V,E) is a distance-based topological index defined as the sum of distances between all pairs of vertices in G. For any integer n, an infinite family of planar and bipartite chemical graphs with cyclomatic number two are constructed such that their line graphs are also chemical graphs, and the difference of the Wiener indices between the graphs and their line graphs is n. This affirms partly an open problem proposed by A. D. Dobry-nin and L. S. Mernikov.
