连通图平均距离的界
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摘要
图的距离和是指连通图中所有顶点间的距离之和,与之密切相关的另一个参数是平均距离,它是指连通图的距离和的平均值。连通图的σ(u)指标定义为图中顶点u与图中所有顶点间的距离之和。利用图的σ(u)指标得到了连通图的平均距离的若干上下界,这些界与图的顶点数、边数、直径和半径等密切相关。
The sum of the distance of a graph is the sum of the distances over all pairs of vertices in the connected graph. Another parameter closely related to this is the average distance,which is defined to be the average value of the sum of the distance. Let σ( u) denote the sum of the distance between the vertex u of the connected graph and all of the vertices of the graph. By making use of this parameter,some lower and upper bounds on the average distance of connected graphs are given,which are closely connected with the numbers of vertices and edges,diameter and radius of graphs.
The sum of the distance of a graph is the sum of the distances over all pairs of vertices in the connected graph. Another parameter closely related to this is the average distance,which is defined to be the average value of the sum of the distance. Let σ( u) denote the sum of the distance between the vertex u of the connected graph and all of the vertices of the graph. By making use of this parameter,some lower and upper bounds on the average distance of connected graphs are given,which are closely connected with the numbers of vertices and edges,diameter and radius of graphs.
引文
卢永红,康淑瑰,孟献青.2013.两类特殊树的距离和及平均距离[J].中北大学学报:自然科学版,34(5):496-499.
卢永红,刘宏英.2010.几类树的距离和及平均距离[J].山西师范大学学报:自然科学版,24(2):16-19.
周涛,徐俊明,刘隽.2004.图直径与平均距离的极值问题研究[J].中国科学技术大学学报,34(4):410-413.
Chung F R K.1988.The average distance and the independence number[J].Journal of Graph theory,12:229-235.
Dankelmann P.2000.Entringer R.Average distance,minimum degree,and spanning trees[J].Journal of Graph Theory,33(1):1-13.
Dankelmann P,Oellermann O R,Wu J L.2004.Minimum average distance of strong orientations of graphs[J].Discrete Applied Mathematics,143:204-212.
Doyle J K.1977.Mean distance in a graph[J].Discrete Math.,17:147-154.
Plesnik J.1984.On the sum of all distances in a graph or digraph[J].J.Graph Theory,8:1-21.
卢永红,刘宏英.2010.几类树的距离和及平均距离[J].山西师范大学学报:自然科学版,24(2):16-19.
周涛,徐俊明,刘隽.2004.图直径与平均距离的极值问题研究[J].中国科学技术大学学报,34(4):410-413.
Chung F R K.1988.The average distance and the independence number[J].Journal of Graph theory,12:229-235.
Dankelmann P.2000.Entringer R.Average distance,minimum degree,and spanning trees[J].Journal of Graph Theory,33(1):1-13.
Dankelmann P,Oellermann O R,Wu J L.2004.Minimum average distance of strong orientations of graphs[J].Discrete Applied Mathematics,143:204-212.
Doyle J K.1977.Mean distance in a graph[J].Discrete Math.,17:147-154.
Plesnik J.1984.On the sum of all distances in a graph or digraph[J].J.Graph Theory,8:1-21.