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The Extremal Cacti on Multiplicative Degree-Kirchhoff Index

Author

Listed:
  • Fangguo He

    (College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China)

  • Zhongxun Zhu

    (College of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China)

Abstract

For a graph G , the resistance distance r G ( x , y ) is defined to be the effective resistance between vertices x and y , the multiplicative degree-Kirchhoff index R ∗ ( G ) = ∑ { x , y } ⊂ V ( G ) d G ( x ) d G ( y ) r G ( x , y ) , where d G ( x ) is the degree of vertex x , and V ( G ) denotes the vertex set of G . L. Feng et al. obtained the element in C a c t ( n ; t ) with first-minimum multiplicative degree-Kirchhoff index. In this paper, we first give some transformations on R ∗ ( G ) , and then, by these transformations, the second-minimum multiplicative degree-Kirchhoff index and the corresponding extremal graph are determined, respectively.

Suggested Citation

  • Fangguo He & Zhongxun Zhu, 2019. "The Extremal Cacti on Multiplicative Degree-Kirchhoff Index," Mathematics, MDPI, vol. 7(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:83-:d:197683
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