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Mathematics 2019, 7(1), 83;

The Extremal Cacti on Multiplicative Degree-Kirchhoff Index

College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China
College of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China
Author to whom correspondence should be addressed.
Received: 22 November 2018 / Revised: 22 December 2018 / Accepted: 10 January 2019 / Published: 15 January 2019
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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. View Full-Text
Keywords: resistance distance; multiplicative degree-Kirchhoff index; cactus resistance distance; multiplicative degree-Kirchhoff index; cactus

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He, F.; Zhu, Z. The Extremal Cacti on Multiplicative Degree-Kirchhoff Index. Mathematics 2019, 7, 83.

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