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Mathematics 2019, 7(1), 83; https://doi.org/10.3390/math7010083

The Extremal Cacti on Multiplicative Degree-Kirchhoff Index

1
College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China
2
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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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. 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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