Further results on the reciprocal degree distance of graphs

被引：4
作者：
Li, Shuchao [1 ]
Zhang, Huihui [1 ]
Zhang, Minjie [2 ]
机构：
[1] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China
[2] Hubei Inst Technol, Fac Math & Phys, Huangshi 435003, Peoples R China
来源：
JOURNAL OF COMBINATORIAL OPTIMIZATION | 2016年 / 31卷 / 02期
基金：
中国国家自然科学基金;
关键词：
The reciprocal degree distance; Bipartite graph; Planar graph; Diameter; Matching number; Vertex-connectivity; HARARY INDEX; TREES;
D O I：
10.1007/s10878-014-9780-7
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
The reciprocal degree distance of a simple connected graph is defined as , where is the vertex degree of , and is the distance between and in . The reciprocal degree distance is an additive weight version of the Harary index, which is defined as . In this paper, the extremal -values on several types of important graphs are considered. The graph with the maximum -value among all the simple connected graphs of diameter is determined. Among the connected bipartite graphs of order , the graph with a given matching number (resp. vertex connectivity) having the maximum -value is characterized. Finally, sharp upper bounds on -value among all simple connected outerplanar (resp. planar) graphs are determined.
引用
收藏
页码：648 / 668
页数：21
相关论文
共 19 条
[1]   Additively weighted Harary index of some composite graphs [J].
Alizadeh, Yaser ;
Iranmanesh, Ali ;
Doslic, Tomislav .
DISCRETE MATHEMATICS, 2013, 313 (01) :26-34
[2]  
Bondy A., 2008, GRAPH THEORY
[3]   Wiener index of trees: Theory and applications [J].
Dobrynin, AA ;
Entringer, R ;
Gutman, I .
ACTA APPLICANDAE MATHEMATICAE, 2001, 66 (03) :211-249
[4]   On the Extremal Zagreb Indices of Graphs with Cut Edges [J].
Feng, Yanqin ;
Hu, Xia ;
Li, Shuchao .
ACTA APPLICANDAE MATHEMATICAE, 2010, 110 (02) :667-684
[5]  
Gutman I, 2004, MATCH-COMMUN MATH CO, P83
[6]   On bags and bugs [J].
Hansen, Pierre ;
Stevanovic, Dragan .
DISCRETE APPLIED MATHEMATICS, 2008, 156 (07) :986-997
[7]   Sharp bounds for Zagreb indices of maximal outerplanar graphs [J].
Hou, Ailin ;
Li, Shuchao ;
Song, Lanzhen ;
Wei, Bing .
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2011, 22 (02) :252-269
[8]   On the reciprocal degree distance of graphs [J].
Hua, Hongbo ;
Zhang, Shenggui .
DISCRETE APPLIED MATHEMATICS, 2012, 160 (7-8) :1152-1163
[9]   DESIGN OF TOPOLOGICAL INDEXES .4. RECIPROCAL DISTANCE MATRIX, RELATED LOCAL VERTEX INVARIANTS AND TOPOLOGICAL INDEXES [J].
IVANCIUC, O ;
BALABAN, TS ;
BALABAN, AT .
JOURNAL OF MATHEMATICAL CHEMISTRY, 1993, 12 (1-4) :309-318
[10]   Four edge-grafting theorems on the reciprocal degree distance of graphs and their applications [J].
Li, Shuchao ;
Meng, Xian .
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2015, 30 (03) :468-488
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