应用数学与基础数学

具有k个悬挂点的n阶单圈图的Harary指数(英)

  • 蔡改香 ,
  • 余桂东 ,
  • 邢抱花
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  • 安庆师范学院青年科研基金(KJ201307)

收稿日期: 2013-12-01

  网络出版日期: 2015-03-29

基金资助

安徽省自然科学基金(11040606M14); 安徽省高校自然科学基金(KJ2011A195,KJ2010B136)

Harary index of unicyclic graphs with n vertices and k pendent vertices

  • CAI Gai-Xiang ,
  • YU Gui-Dong ,
  • XING Bao-Hua
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Received date: 2013-12-01

  Online published: 2015-03-29

摘要

连通图的Harry指数定义为所有顶点对的距离倒数和.本文对具有k个悬挂点的n阶单圈图的Harary指数进行了研究,并给出了此类图中具有极大Harary指数的图类.

本文引用格式

蔡改香 , 余桂东 , 邢抱花 . 具有k个悬挂点的n阶单圈图的Harary指数(英)[J]. 华东师范大学学报(自然科学版), 2015 , 2015(1) : 120 -125 . DOI: 10.3969/j.issn.1000-5641.2015.01.014

Abstract

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the graph with the largest Harary index among all the unicyclic graphs with n vertices and k pendent vertices were investigated.

参考文献

PLAVSICD, NIKOLICS,  TRINAJSTICN, et al. On the Harary index for the characterization of chemical graphs[J]. J Math Chem, 1993, 12: 235-250.
IVANCIUC O,  BALABAN T S, BALABAN A T. Reciprocal distance matrix, related local vertex invariants and topological indices[J]. J Math Chem, 1993, 12: 309-318.
DAS K C, ZHOU B,  TRINAJSTICN. Bounds on Harary index [J]. J Math Chem, 2009, 46: 1369-1376.
ZHOU B, CAI X,  TRINAJSTICN. On the Harary index [J]. J Math Chem, 2008, 44: 611-618.
YU G, FENG L. On the maximal Harary index of a class of bicyclic graphs [J]. Util Math, 2010, 82: 285-292.
BALAKRISHNAN R,  SRIDHARAN N, IYER K V. Wiener index of graphs with more than one cut-vertex [J]. Appl Math Lett, 2008, 21: 922-927.
CHEN D, The Harary index of a unicyclic graph (in Chinese) [D]. Master Thesis. Changsha: Hunan Normal University, 2009.
FENG L, ILI\'{C} A, ZAGREB, Harary and hyper-Wiener indices of graphs with a given matching number [J]. Appl Math Lett, 2010, 23: 943-948.
HE C H, CHEN P, WU B F, The Harary index of a graph under perturbation [J]. Discrete Math Alg Appl, 2010, 2: 247-255.
ILIC A, YU G, FENG L, The Harary index of trees [J/OL]. arXiv preprint arXiv: 1104.0920 [math.CO], 2011.
XU K , TRINAJSTI\'{C} N, Hyper-Wiener indices and Harary indices of graphs with cut edges [J]. Utilitas Math, 2011, 84: 153-163.
WIENER H, Structural determination of paraffin boiling point [J]. J Amer Chem Soc, 1947, 69: 17-20.
DOBRYNIN A,  ENTRINGER R,  GUTMAN I [J]. Acta Appl Math, 2001, 66: 211.
XU K, DAS K C, On Harary index of graphs [J]. Discrete Appl Math, 2011, 159: 1631-1640.
DAVID G, SEMMES S. Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure [M]. Oxford Lecture Series in Mathematics and its Applications. Oxford: Oxford Univevsity Press, 1997.
COOPER D, PIGNATARO T. On the shape of cantor sets [J]. J Differ Geom, 1988, 28: 203-221.
WEN Z X, XI L F. Relations among Whitney sets, self-similar arcs and quasi-arcs [J]. Israel J Math, 2003, 136: 251-267.
RAO H, RUAN H J, XI L F. Lipschitz equivalence of self-similar sets [J]. C R Math Acad Sci Paris, 2006, 342: 191-196.
FALCONER K J, MARSH D T. Classification of quasi-circles by Hausdorff dimension [J]. Nonlinearity, 1989, (2): 489-493.
FALCONER K J, MARSH D T. On the Lipschitz equivalence of Cantor sets [J]. Mathematika, 1992, 39: 223-233.
XI L F. Lipschitz equivalence of dust-like self-similar sets [J]. Math Z, 2010, 266: 683-691.
RAO H, RUAN H J, WANG Y. Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios [M]. Trans Amer Math Soc, 2012, 364: 1109-1126.
XI L F, RUAN H J. Lipschitz equivalence of generalized {1, 3, 5}-{1, 4, 5} self-similar sets [J]. Sci China Ser A, 2007, 50: 1537-1551.
XI L F, RUAN H J, GUO Q L. Sliding of self-similar sets [J]. Sci China Ser A, 2007, 50: 351-360.
WEN Z X, ZHU Z Y, DENG G T. Lipschitz equivalence of a class of general Sierpinski carpets [J]. J Math Anal Appl, 2012,

385: 16-23.
XI L F, XIONG Y. Self-similar sets with initial cubic patterns [J]. C R Math Acad Sci Paris 2010, 348: 15-20.
XI L F, XIONG, Y. Lipschitz equivalence of fractals generated by nested cubes [J]. Math Z, 2012, 271: 1287-1308.
LI B M, LI W X, MIAO J J. Lipschitz equivalence of McMullen sets [J]. Fractals, 2013, 21: id. 1350022.
LALLEY S P, GATZOURAS D, Hausdorff and box dimensions of certain self-affine fractal [J]. Indiana University Mathematics Journal, 1992, 41: 533-568.
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