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Some transformations on multiplicative eccentricity resistance-distance and their applications

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  • Hong, Yunchao
  • Zhu, Zhongxun
  • Luo, Amu

Abstract

For a connected graph G, the multiplicative eccentricity resistance-distance is defined as ξR*(G)=∑{x,y}⊂V(G)ɛG(x)·ɛG(y)RG(x,y), where εG( · ) is the eccentricity of the corresponding vertex and RG(x, y) is the effective resistance between vertices x and y in G. A connected graph G is called a cactus if any two of its cycles have at most one common vertex. Let Cat(n; t) be the set of cacti possessing n vertices and t cycles, where 0≤t≤n−12. In this paper, we introduce some edge-grafting transformations which decrease ξR*(G). As their applications, the extremal graphs with minimum and second minimum ξR*(G)-value in Cat(n; t) are characterized.

Suggested Citation

  • Hong, Yunchao & Zhu, Zhongxun & Luo, Amu, 2018. "Some transformations on multiplicative eccentricity resistance-distance and their applications," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 75-85.
    • Handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:75-85
    DOI: 10.1016/j.amc.2017.11.055
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    References listed on IDEAS

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    1. Huang, Jing & Li, Shuchao & Li, Xuechao, 2016. "The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 324-334.
    2. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
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